I'm not going to say bless you to the girl in the cubicle behind me
Why would you not want to say bless you?
I think it just becomes annoying after a while, she always says thank you
That can get repetitive. Saying bless you is common courtesy, but it's okay if you don't say it every time. She might appreciate it when she doesn't have to say thank you.
I don't see the point in it.
Well maybe you can cap yourself at once a day. That way she knows you are considerate, but it's not over the top.