I'm not going to introduce my gf to my mother
Why would you keep from introducing your girlfriend to your mother?
My mother is always rude towards people I know
You shouldn't introduce people to toxic people you know. If you know your mother is toxic then it's best to avoid the situation.
Should have expected as much from a gf like her.
It is probably a good idea to give it some time before introducing your girlfriend to your mother. It is also probably smart to tell your girlfriend why you are doing this so they do not get the wrong idea.