Episode 2:
I keep feeling like I've seen this plot before. Definitely not The Twelve Kingdoms, of course, although it also had a Japanese girl being forced into another world, where she was considered special in some way. I am pretty sure that the thing with "hand in the bathroom, that gets interrupted" was present in some show a couple of seasons back. Not sure if that was an anime, though. I was also somehow reminded of Spellbinder. Considering that that series and source manga both came out in 1995, that makes sense. Somehow. I guess.
While the show itself is not bad, it feels like it will be "I am a modern person, I know how to make the ancient society better, but I will constantly be a victim screaming at the top of my lungs". And gods, Yuri's voice is annoying. I will give 1 more episode a chance, but it will need a proper hook for me to stay.