Is it strange that I hang out with my ex?

I broke up with my ex boyfriend a few months ago and got with my current girlfriend a week later. I dated the ex for about 6 months but broke it off because I didn't feel being with a guy is who I really am. Anyways, he comes in my work and we talk sometimes, because it is the closest store that is open at night. I went bowling with him once and he and I ate with my girlfriend (which made her break up with me, but we got back together). I got him a huge discount on a $1700 TV and he had to use my car to take it to his barracks, so he filled the tank up because it is a long drive there and back. My girlfriend thinks it is weird that he did that and we hang out and talk so soon after I broke up with him and doesn't want to see me for a while. Is she right? Is it weird I talk and hang out with my ex?