Some one who is asexual, not in their gender but their sexual orientation. A person who is not attracted to guys, girls, or anything thereof... Bears usually do not register attractivness, hottness, like talking about sexual topics, think the "hot" guy in school is "hot," or have a desire for any sort of sexual activity. Bears are not very common, in fact less than 1% percent of the US population are true bears. Being a bear is in no way a negative; nor does the term bear have any negative conotation.
"Are you gay or straight?"
"Neither, I'm a bear."