She said he asked her to get in the bath and she said no. But she thought maybe it was okay because he is still young enough or maybe if she wore a bathing suit. I told her no under any conditions. The next night I came home and she said he asked again so maybe I wanted to explain it to him. Again I thought it was inappropriate and she should know the answer is no and how to handle it. Now I am really uncomfortable and worried she has no sense of boundaries and should find someone else.

I see no boundary issues at 2.5; it's totally innocent. I also see no reason for a nanny to get in a tub with a 2 year old just because he wants her to. Have her tell him that she doesn't want or need a bath or to get wet just then and that she has work to do after his bath. There's no reason for you to have to explain.

Many parents would bath with a 2 1/2 year old, and often if the nanny is a live in and the child almost views them as a mother figure I can see them asking. Children do ask this often, so it is normal for them to ask.

Now I am really uncomfortable and worried she has no sense of boundaries and should find someone else.
I'm thinking, since she brought this to your attention, her sense of boundaries is okay. If they weren't, she would have stripped and jumped into the tub with your son without saying a word to you.

Make sure she understands that adults don't give a positive answer to every request a child makes. In fact, adults don't even have to explain when they say no.