It is inappropriate to call people names in public. It is distasteful. What this isn't is sexism, and it's certainly not offensive to the entire female gender.
Is that still under debate? Would you be able to say "bitch" in front of your mother and not feel uncomfortable?
I am not a native speaker, but I think "bitch" is actually just the word for a female dog. What makes it a swear word is in the imagination and value system of the receiver.
It would probably be wise to never use derogatory words for other people in general. But that doesn't seem the way the human psyche is set up.