First thing's first, we want to be presentable. I know we're playing an outsider Mongolian princess in Rokugan, but Sarnai has also been on the road for three weeks with little in the way of proper accommodation. Getting cleaned up isn't just a way for her to relax, but also a way to ease introductions with her peers. She's not hiding who she is, nor should she. She's got a scimitar instead of a katana and her clothing is of a noticeably different style than those common amongst the Clans.
But by keeping clean she's sending a message. "Yes, I am as Rokugani as the rest of you. I care about staying clean, about preventing the spread of filth or, even worse, disease from staining the things I touch." And by doing this they must acknowledge, on some level, that the stereotypes of the Unicorn as uncultured barbarians are exactly that, stereotypes. A small shift, perhaps, but a hundred small shifts can help bring Sarnai's peers around to the fact that though her Clan's ways are different that doesn't mean they're inferior.
In Rokugan all things have multiple layers of meaning. In this way we create a small bridge of common values, and doing such things is going to be important if we want to show the worth of the Clan of Shinjo.
[x] Find a bathhouse. You have had a long, hard journey to get here, and you could most assuredly do with a chance to wash and relax. A hot spring or a sauna sound absolutely divine right about now, and you may well encounter some of your rivals from the more distant clans within, for much the same reason.