I recently met a girl who is 22, and she said she never had a bf, and she doesn't want. She will never had one, because she doesn't like the idea.
I went out with her a few time, just as a friend and nothing more, I believe that she is very shy, although I could make a lot of conversation with her. She doesn't like bars and clubs, she doesn't like to draw attention to herself.
Generally speaking she never wants a relationship in her life. She thinks the idea of kissing is gross. How is that possible?

Sounds like she's had some experiences in her life that may have contributed to this fear of relationships, commitment and sex.

Do you know of anything that may influence her to act this way?

Most of the girls I've run into that have these issues already have a few pre-existing issues in life that they’ve had to overcome like: abuse (sexual or otherwise), a bad relationship, shitty family life, traumatic event etc.
This is a wiring that is ingrained deep into the people it occurs in and its hard enough to understand the issue much less get them to change.

You are trying to see where you can take this with her right? I would be really careful and tread lightly for a while because somebody who is opening up to you about being against dating/sexual contact is somebody you are going to have to put some effort in to. Otherwise it seems she wont budge anyways.

So basically be prepared to either A. understand the situation and be supportive B. Consider other options and/or be a friend and nothing more.

“A” is a commitment, and I wouldn’t recommend it to be honest.
“B” is the best way to stay connected with her (even if it means friendzoned…but it doesn’t look like shes trying to go any further with ANYBODY at this point) while also looking elsewhere and not getting tied down to a dire situation.

Good luck man.