He laughs again. "We are very proud of it. Now let Us show thee the bath, then," he says, and leads the way out.

"Okay! Thank you."

It's just a couple of doors down, a large room the center of which is dominated by an empty tub. There is a mechanical contraption attached to a wall with a lever that the dragon pulls on so that water starts flowing through a set of pipes that go all the way to the bathtub itself. As soon as the bath starts filling, the smooth black rocks under it start glowing faint red symbols, which instantly brings the water to a pleasant toasty temperature. 

Having demonstrated this, he releases the lever and pulls a different one next to it, which drains the water. "All of this except for the stones under the tub is purely nonmagical," he explains cheerfully. "We acquired it from an inventor from across the sea—ah, but We forget ourselves. We shan't begin any tales now."

"Reasonable and responsible, but I will be wanting that tale, because that is extremely cool and I want to know all about it."

"As thou wishest," he says, grinning. "We do not have ladies-in-waiting to help thee bathe, unfortunately, and somehow We think a dragon-in-waiting would not be quite the same, so We shall prepare thy supper while thou recuperatest."

Snort! "Yes, thank you. It's mostly the clothes that need a lady-in-waiting instead of the bath itself, I'm perfectly capable of not drowning in a bathtub. But as long as everything has buttons I can reach, I will be fine."

"We hope they will be to thy liking. We shall see thee anon," he says, bowing with a hand behind his back.

"Thank you kindly," she says, with a returning curtsy.

Okay, off to investigate her clothing situation! Is she going to have an outfit that is mostly appropriate for a princess, except for how all of the fastenings are where she can herself reach and thus seeming like she's terribly low class?

Relatedly: are there towels and soaps and oils available?

Yes to all, though the style of the fastenings is such that they're mostly hidden. 

There are also some clothes in foreign styles unlike what she's used to, that don't really register as either low or high class: long dresses (robes?) made of silk or cotton, with strange ribbons that are clearly paired but whose manner of attachment to the dress is not obvious, floral patterns in golden thread, manners of dress that she may have heard described from descriptions of realms far away but never personally seen before.

She will stick to clothes she understands for now; experimentation of fashion will be for later. She'll need to ask questions about them before being able to wear them with any competence, after all. For now, she picks out something in a color that goes well with her hair, and then she can see about ~having a hot bath~.

Has she mentioned that tournaments are very dusty? Because they're very dusty. And even though she was under shade for nearly all of it, she was outside for nearly the entire day. Which, predictably, built up some sweat, giving the copious dust something to stick to. She'd kept her face and hands clean, of course, but it's not the same thing as being clean. So this is great. Normally she wouldn't be washing her hair so soon, but the soaps are delightfully gentle, and one of them smells very, very nice, and Svetlina did not locate a hairbrush before her bath, and her scalp is very icky. So. Hair washing just kind of happens.

Eventually, she emerges from the bath and goes looking for a dragon and food, damp and well-dressed and happy.

There's a delicious smell wafting from somewhere...

Eeeeee of course the experiences hoarding dragon would also become a good cook, it's so obvious in retrospect!

She's going to follow her nose, of course.

Her nose leads her to a small dining room that could seat no more than some ten people, with a similarly small feast of pheasant, venison, and wild boar, plus bread, wine, and fruit.

The dragon himself was seated, but he stands up when she enters the room and bows. He's wearing a different suit than the one he had been prior to her bath (which was itself also not the jousting armour he'd worn before turning back into a dragon). "We trust thou hast enjoyed thy bath?"

She's definitely looking very happy; she practically bounces into the room, in her new dress and with her hair up in a different (simpler) style.

"Hello! Yes, it was fantastic, your soap is better than what we have at home. And the - being able to just have water was excellent, I would love to hear about how that works!"

"We would like nothing more than to tell thee all about it. Please, sit," he says, gesturing.

She does, grinning at him. And also maybe grabbing a little bit of fruit to nibble. While clearly waiting for him to tell her about his hoard.

"So that particular contraption was invented by a human scholar some seventy summers ago. He lived across the Eastern Sea, in the Empire of the Golden Sun. He was the Jade Emperor's twelfth son, so he would inherit no titles and not be allowed to marry, but he could live out his life in comfort and peace. He also did not, particularly, want to inherit or marry; his interests were more academic and he had eyes only for men, not women."

He serves her and himself some of the meat and bread as he speaks, absent-mindedly.

"Huh!" she says, chewing on both the delicious food and the concept of men preferring other men to women. It sounds convenient for this guy in particular? Hooray for him?? (How many other people are in less convenient for them situations of same?) "Does the whole empire have this technology, then? Or among the nobility?"

"Ah, unfortunately not. It requires a water source at a higher altitude, so it only works in or near mountains. The pipes he had to build were very long and are expensive to maintain, but it's much easier here in Our den, when We can get water from the springs that run through the caves."

"Oh. So, like aqueducts, but for... interior water instead of irrigation."

"Exactly right! And the Empire has numerous springs where the water runs hot, so they do not need magic for that, whereas We had to improvise."

"See, that one seems like the kind of magic humans could manage? Get some rocks in an old growth forest, enchant them to heat up water. It's perhaps not very scalable, but I don't see why we couldn't manage it. I suppose there might be a way to make the water thing work as well, and that might scale better, but you'd need to get the water to a storage tank above everything, or something." ... Hmmm. Great, now she wants to run water and piping experiments...

"Thou wouldst get along great with the Prince, We believe. He was running such experiments when We first met him. It was part of why We decided to join his harem."

"Hmm, well, if nothing else I'd love to look at his notes if you have copies of them..."