I don't really know how to give you back your faith in humanity, because I have very little left myself. But to say where to start...
Well, don't try to find a girl in a bar. Anywhere else but a bar. Perhaps a private party of a friend's or something. Try to take things slow, don't rush into a relationship or into sleeping with anyone. And be serious with her if you want her to be serious with you.
If everything in your relationship is where it should be, neither of you really have no reason to sleep around. If a person is in a relationship and cheats given the opportunity, it's not a good relationship. They can fool themselves into thinking it is, but it's been dead or dying for a long time. The only time I ever wanted to cheat one of my exes was when I already knew the relationship was over. Even knowing that I didn't do it. I wouldn't have only cheated him, I would have been cheating on myself, if you know what I mean. I could never have forgiven myself if I had done that mistake, and in retrospect I'm really glad I never took that step.