How to stop being friends without causing an argument?

(this may be long and I cannot say anything outright as last year I was bullied and want to avoid conflict again)

There is a girl in my class and she sits next to me, talks to me and follows me to sit with my friends who I have known for a long time. At first, I thought she was nice and enjoyed her company. Now, she is a self righteous, nasty person. She will have a go at you if you do not agree with her, even petty things like film taste! She makes awful comments , including one about special needs people. I was joking around, saying I'm sick of cleaning animal mess and she screeched you shouldn't have an animal if you can't handle it! and I said I'm joking? I love my animals and, although I may not enjoy it, I keep them clean. I can not take her horrid comments and listen to her yelling at people for nothing. My mum said to not argue with her because she is the type to make my life hell. I asked my friends for advice and they said gradually cut her out but I can't. She follows me everywhere and when I hang out with my mates, she sits there and ignores everyone (she isn't shy and she goes in there a lot) all I can think of doing is next time she says something offensive, to say it offends me and see what happens. If I am honest, I blame myself for letting her think she can get away with this nastiness and putting up with it. Anyone got any advice? I am at the point where I WILL argue with her, not caring about the consequences.

Thank you.