She'll be happy to get to know him right back! Having faction friends is a major plus in her book, and any connections she can make, she wants to, as well as letting people know there's someone who won't overcharge them to treat them.

And as far as her youkai goes, I'm sure it'll come up sooner rather than later. Izo's a close friend of hers, so she knows exactly how hard it is trying to ask him about things that he's not talking about. She can even step back and let the tengu talk to give Ryouma an expert opinion!