My best friend invited me to a car race. I said I will find out if I can come and let her know, so I asked my mum and she said if you want to. So I said to my Best Friend that I will think about it and look and see if I am free. Her mum asked me if I can go but I said not sure because it isn't clear if I am free, but I turns out I have got to go to a party and my Grandma is having a big party where all of my family is coming, even the ones I have never seen before.

So I text and say really sorry but I can't make it, she texts back saying you are kidding how long has it been planned for, so I say I'm really sorry again and explain why.
She then texts back saying you already said you can come and don't you know friends aren't supposed to bail on each other.

Do you think I have bailed on her?
And what should I do forget about it and be friends or not be friends any more

You never told her that you were definitely coming, you said you would have to check if you were free.
I'm sorry but family comes before friends in my book.

If she does not to be friends anymore over something petty like this then she is not worth being friends with.