I'd say watch yourself and don't let it go that far, but if you think it's a real possibility, it's definatly not safe without knowing where she's been.
I heard on a show, "talk sex with sue johanson" (love that show... hehe) that when a couple was starting to spend more time together, she recommended the W to tell the H something like this "As we start spending more time together, i think there is a possibility of us taking this further than expected. I trust you, but I'm not sure about OW (OM in your case). Maybe we could both go get checked out just to be safe"
I don't know. Good luck, hopefully you can get some better advice than mine...
If i can't fall in love... I'd like to fall in chocolate! ~ Author Unknown