I'm not going to tell my girlfriend that I used to date her best friend
Don't you think she might find out eventually?
I'm not sure she'll realise it anyways
If you think that this might be something that would upset your partner you shouldn't be keeping a secret from them. Just because you have the idea that it might hurt their feelings doesn't mean it's right to hide something from them.
Is it really that bad if I don't tell her?
Yeah it can be bad. If you don't feel comfortable, you should take your time. Also if you hand out with her bestfriend and she finds out she might be suspicious.