Why Does My Cat Bite Me?

My barn cat thinks a good interaction with somebody ends with a bite.

One time I was playing with her and I was being really careful not to provoke her to bite, eventually I decided to leave and she acted quickly to give me a tiny careful bite that didn't even hurt. It's like she understood I was being careful and she was careful too.

I have both of my house cats trained to do "special behaviors" to get fed (tapping with a paw in one case, head-butting my fist in the other case) This involves finding a behavior that they would do anyway and feeding them when they do it. Cats find it really meaningful.

I know I could teach my barn cat to bite for food but that's obviously a bad idea.