I like this guy, what should I do?

So up until this point I have only dated women, admittedly rather unsuccessfully. And, I have finally come to the realization that I am bisexual. This was something that was difficult for me to come to terms with, and I wasn't even really sure about it until I started this new job.I am working very closely with this guy who I believe is gay. What makes me think he is gay, is that he has very detailed discussions about Rue Paul's Drag Race, and Project Runway with a female coworker of mine. He also has certain mannerisms. His roommates are all females. And, there is also this unspoken understanding among my co-workers that he is dating a former male employee. I however, am not sure. My gaydar is pretty horrible. You know, why can't you be straight and like runway as well or why can't you be gay and like football etc.??Anyway, I am really attracted to him, and I get the feeling he is attracted to me, but it may just be me. The main thing that leads me to believe that there is a spark, is that at times when we speak to each other there is this really intense eye contact, and it's a real turn-on haha. But, who knows if he's feeling this as well. Flirting is limited as we work in a fairly stuffy office. But, he does invite me out to lunch and on walks occasionally. I think this shows he may like me, but he could also just be friendly and sociable? And, I think I once caught him looking at my butt. Anyway, I have never felt attracted to another human being like this before let alone a guy. It's driving me crazy. I want more. The kicker here is, if he is gay, I believe he has a boyfriend. And this will sound bad, but I am hoping he is shallow bc I feel I am more attractive than his current bf. So, what should/can I do?