"Oh! Princess! What a delight! I wasn't expecting to see you here today!"
Celestia smiled at Dusty Pages' welcome, as she always did. The Library of Canterlot might not be a place she visited frequently, but there was no denying that she enjoyed coming here. As expected of course, there was the usual case of ponies bowing to her, shocked that the Princess herself had graced them with her presence. Celestia likewise gave nods and waves to each of them, all while making her way over to her old friend's desk. Eventually she managed to get there, and after glancing around and seeing ponies get back to their books, she smiled to the aging mare beside her. "I trust the day finds you well, Dusty?"
A quick chuckle from the elderly earth pony mare. "Oh, as well as it usually is. Things are quiet of course. I make sure of it." The sound of a sudden and loud sneeze from somepony nearby emphasised that point, as Dusty narrowed her eyes to the unwitting perpetrator, who covered their nose and blushed with embarrassment.
Giggling with some amusement, Celestia leaned closer to her. "I'm glad to hear it. In all my long years, no librarian has ever managed to keep this place in order as well as you."
Dusty bowed her head to her. "You honor me, Princess. Now, I assume you're here for a book?"
Celestia glanced around. "Oh, nothing in particular. Any light reading you can recommend would be welcome. I have some free time this afternoon and I figured a good book would be the best way to pass it by."
Dusty nodded, whipping out an old and tattered-looking tome and flipping through the pages. "Let's see...ah! I think I have just the thing!" Setting the book aside, she clapped her hooves, a sound which echoed across the rest of the library, before smiling to Celestia. "Just wait right there and my assistant will be here to bring the book to you."
Celestia looked to her with curiosity. "Oh? You finally found somepony to fill the assistant role?"
Dusty nodded to her, smiling. "Indeed. It took a while, but I finally managed to find somepony who met the library's standards." She chuckled. "Though I really shouldn't have been all that surprised. Why, she's been coming in here and loving this library since she was only a filly."
Celestia started to smirk a little. "Ah, I'm guessing this is that 'model member' you kept mentioning to me from time to time?"
Dusty opened her mouth to reply, only to stop when, all of a sudden, both she and Celestia were taken aback by the sudden arrival of a towering pile of books floating in from the side. A quick glance revealed it to be held aloft by an aura of pinkish-purple magic, with a mare standing just behind the books, her face obscured by the collection. "Don't worry, I'm here. I just needed to get the new collection in proper order."
Dusty smiled to her. "That's quite alright, Twilight. Just set them there for the moment. We have a rather immediate request to deal with first."
Here, Celestia watched as this new mare, Twilight, did indeed set the books on the desk as instructed. The young unicorn was smiling happily, clearly in her element, and looked again to her employer. "Of course, Miss, Pages." Then she looked to Celestia finally. "So, how can I...help...you?" Slowly, her eyes widened, and she only now realised who it was that had been standing beside her since she arrived.
For Celestia's part, she gave a smile to this clearly-awestruck young mare. "A pleasure to meet you, Miss Twilight."
After a time, Twilight started to inhale and exhale, both very loudly and very frequently. As if on instinct, Dusty offered her a paper bag from across the desk, which Twilight graciously accepted. Celestia watched, half amused and half worried, as this young mare used the bag to try and cope with her hyperventilation. She was used to having ponies be excited or nervous around her, but this was definitely taking it to a new level. Eventually, Twilight managed to calm down enough to set the bag aside and actually say something to her, albeit in a somewhat disjointed manner. "I...Princess...you...Celestia...visit here?!"
A quick laugh from Celestia. "I assure you, I am just as much of a lover of books as any other pony. In fact I came here for one in particular, if you'd be so kind as to find it for me."
Realising that she had a job to do, Twilight blushed fiercely, then looked back to Dusty, who pointed to the book's name in the tome she'd been using earlier. With her ears perking up, Twilight finally smiled to the document. "Ah! Of course! If you'll just give me a moment." She darted off, no doubt heading down a route she knew by heart at this point, and Celestia watched as she moved with expert speed and precision. It was like she was homing in on the desired book, and before long she'd managed to whip it out of its shelf, before promptly zipping back to the expecting royal. "Here you go, Princess!"
Accepting it, Celestia smile to her. "Thank you, Twilight. I don't suppose you'd care to join me for a quick stroll while I head back to the palace?"
Twilight's face went as white as a sheet, and she began her now-expected degree of blundered speaking. "Oh, I couldn't possibly...that is to say...it would be most improper to..."
"Oh for the love of...it's fine, Twilight!" Dusty remarked. But as her protégé looked to her, ready to speak in response, the older mare halted her. "Ah! I don't want to hear it! You've worked enough for now, so I'd say you've earned a break for a bit. Besides, getting to walk with a Princess is a rare honor."
Twilight nervously looked from one mare to the other, with Celestia in particular looking very amused about all this. After a time, and after gathering some semblance of confidence, Twilight sighed, giving a deep bow to her monarch. "Princess, I'd be delighted to accompany you."
Smiling, Celestia bowed back, then trotted over to Dusty's desk. "In that case, I'll need this checked out." Taking the book from her, Dusty went through all the usual motions of letting a book out, just as she'd done a million times before, after which she offered it back to her. Now with the book officially hers for the time being, Celestia turned to leave. "Come along, Miss Twilight." She could see Twilight hesitating through the corner of her eye, but the younger mare eventually began to follow, much to Celestia's delight. The two exited the library, and as they descended the stairs, Celestia spoke again. "Have you and I met before?"
Twilight paused, thinking on that with some confusion. "Um...no, I don't think we have."
Celestia considered that. "I could've sworn I heard your name mentioned to me once before, many years ago." Then her smile widened. "Ah, I remember now. You were hoping to enter my school, yes?"
Here, Twilight's ears drooped slightly. "Oh, that. Yes, I did try to enter, but...I suppose I just wasn't in the game that day."
The Princess looked back to her. "You needn't be so hard on yourself, Twilight. A dragon egg is no easy task. Few, if any, would have been able to do anything with it."
The words weren't as comforting as Celestia had hoped, judging from Twilight's continuing low tone. "It's just...I'd dreamed of getting to be in that school for ages at the time. Ever since I first saw you raise the sun at the Summer Sun Celebration." She looked up to her. "I wanted to learn all I could about magic, and even after I failed to get into the school, I studied as much as I could."
Celestia nodded. "I'm sure you did. You don't strike me as the kind of mare who'd quit learning simply because of one setback."
To that, Twilight's smile finally returned. "Oh, I promise you, I didn't. With my friend Moondancer, I found every magical textbook I could get my hooves on, and we studied night and day together. I learned so much. My friends kept going on about how many wonderful spells I knew by the time we'd all gained out cutie marks. Me personally? I was just happy to have learned them."
Celestia thought fondly on that. "I'm glad to hear of it. Enthusiasm for magic is rare these days, at least to the degree you seem to have displayed for it."
Twilight took a deep breath, feeling at least a little bit more relaxed than before. "I still wonder what kinds of wonderful things I could have learned at that school though."
Celestia chuckled, causing Twilight to look back at her as she spoke. "I wish you had entered. It would have been nice for a filly that age to show that kind of interest in the higher spells. Most students just get put in by the more noble families so they can brag to their neighbours about it."
Twilight felt the need to stifle a laugh at that, lest she seem improper about the whole thing. "Well, if nothing else, I should thank you for creating a school like that in the first place, Princess. So many unicorns have been helped by its teachings."
A long sigh from Celestia. "Yes...but still, it would have been nice if..."
Twilight saw the way she just stopped mid-sentence, then curiosity got the better of her. "What would have been nice?"
Maybe it was her earnest demeanour, or maybe it was some feeling Celestia had about her, but whatever the case, the Princess suddenly felt at ease in confiding in her. "For many years, I have sought not just students in general...but a student. My student."
Twilight halted dead in her tracks, her eyes wide. "You...you wanted an apprentice?" When she saw Celestia nod back to her, her mind raced. "A...a chance to learn magic from Princess Celestia herself?! That would be the greatest opportunity in Equestrian history!"
Celestia smiled. "I wouldn't go that far. But...I do wonder if there will ever be a time when I can impart all I know on one willing to learn and grow. A thousand-year rules leaves a lot of experience to give after all."
Calming down from what she'd learned, Twilight smiled back to her leader. "Well, if the day should come when you do find one who is worthy, I have no doubt that they'll begin the most wonderful time of their life."
Celestia gave a slight bow of her head to her. "You're very kind to say so, Twilight, and I appreciate it." Then she craned her neck upwards, glancing to the sight of the palace, which was only now coming into view. "Well, I believe this is where we part ways."
Twilight bowed to her. "It's been a pleasure, Princess."
Celestia nodded. "The pleasure was all mine. And perhaps we shall converse again one day. This was quite nice."
"Yes, it was, and I'll be sure to treasure the memory of it," Twilight answered back. "Though, between you and me, it's something I would have totally lost my mind over back when I was a filly."
The two laughed together, but when it ended Celestia watched as Twilight took a few steps back, before finally turning and making her way back to the library. Celestia watched her go, taking in all that she'd learned about that young mare. Then a smile came to her face, and she nodded slowly. "Oh Twilight...what a fine apprentice you'd have made."
Author's Note
It always seemed odd to me that, in all those alternate realities that Twilight and Spike went to in the season five finale, they never met any differing version of Twilight herself. So, figured I'd try to come up with a take on her myself 
