I'm going to bail on my friend's birthday event
Has your friend let you down in someway?
Many times. She makes me feel very bad every time I'm around her
That's not nice if your friend is always making you feel bad, but you got invited on her birthday and you should come. I would recommend that you spend the time on that party to try to fix your relationship with her and make sure to tell her that you always feeling bad around her is not okay and if you want your friendship to continue you should make an effort to do so.
I feel that effort would be in vain
If you don't go maybe talk to her and explain how you feel. Sometimes friendships just don't work out and need to end.