I don't want to be around my best friend's girlfriend
Why don't you want to be around her?
I'm totally interested in her and I don't want it to show.
You may want to take a break until you can sort your feelings out. It's wrong to ask your friend to chose between you and his girlfriend.
Well, I could go to the gym until then.
That's a good idea. However, eventually your friend will wonder why you avoid his girlfriend when they are hanging out so you will have to come up with an excuse.