I agree that there are bullying behaviours involved, but bigot is much more accurate in this case.

A bigot is defined as "a person who is obstinately or unreasonably attached to a belief, opinion, or faction, especially one who is prejudiced against or antagonistic toward a person or people on the basis of their membership of a particular group."

Whereas a bully is defined as "a person who habitually seeks to harm or intimidate those whom they perceive as vulnerable."

Both are true, but bigot provides much more necessary information in this context.