I don't think Abbie is gay or bisexual because she's not attracted to men physically imo. That's jumping the gun to one very unlikely possibility. She's probably just asexual and you can read more about it here: http://en.wikipedia.org/wiki/Asexuality
She probably falls into the category of heteromantic. "Heteroromantic: romantic attraction towards person(s) of a different gender – the romantic aspect of heterosexuality." I could be wrong about this, but I don't think it's fair to call someone homosexual or bisexual simply because they lack physical attraction to the opposite sex.