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.
I think the idea of swearwords in general is to be derogatory. Would you be comfortable saying "shitface" in front of your mother?
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.