I don't want my gf to know my online banking password.
That is very personal information. Did she ask you to tell her your password?
No. I just think she might and I don't want to get into a fight over it.
It's understandable that you wouldn't want her to know the password to your bank account. Financial independence in a relationship can help both parties feel more comfortable. It doesn't sound like there's any reason to believe she even wants to know your password though.
Well I can't be blamed if I keep it to myself!
You should always keep passwords, especially to something as important as your bank account, to yourself. Sharing it with other people, even loved ones, can lead to nefarious people gaining access. You should not feel pressured to share your password.