There's the conventional old "don't do it, he's just trying to use you to experiment with and you'll end up sad afterwards" answer. And it's true, maybe if you do something with him he'll be all weirded out and pull away and you'll be all distraught and stupid about it. And yes, you'd be a party to his cheating on his girlfriend, so if she found out and they blew up then you'd probably feel that weighing on your conscience.
But here's another angle. If he's asked you to try something, then turning him down after he's put himself out there could strain your friendship just as much as if you said "okay." He could feel embarrassed, exposed, etc.
Also, as far as his girlfriend goes: she might know that he has this experimental side and (while it's a long shot) support it, and endorse him sleeping with another guy if it sorts his shit out. Maybe she wants him to find out for sure before they get in any deeper, rather than spending years with the guy only to find out after her uterus has dried up that he'd rather be with another guy. Or she might have no idea, but if he's asked you it sounds like that relationship is precarious anyway. If he doesn't cheat on her with you, he might cheat on her with someone else to explore his bi-curious side. So the "other man" can be unwitting about it or he can know exactly what the score is- either way, she's going to end up at the same point, and I'd contend that the bulk of responsibility for it will be with her experimental boyfriend.
So the way I see it your choices aren't just "do it and be miserable!" or "don't do it, move on and find someone else who'll make you happy!" Actually, you could do it and he could like it so much that he leaves her for you. Or you could do it and sure enough, he might be all awkward afterwards and you could drift apart and then you'd have that lost friendship getting you down... but you'd have gotten one good romp out of it, which is more than you get if you say "no, I can't" and he still gets awkward and you drift apart. And his girlfriend could either be fine with it or she could hate you; but if he's likely to cheat on her sooner or later, and she's bound to end up hating somebody, why not have your romp and let it be you? You probably won't have to deal with her long after their relationship goes to hell, if he's the only connection you have with her. Or you could say no to him and lose the relationship anyway. Or say no and continue to pine for him until he experiments with someone else, and then you're jealous, too. Or say no, back off and you probably get over him in time. Probably. Except you might always wonder.
Call it rationalizing or call it a cost/benefit analysis, but I don't see where you stand to lose a whole lot more by having sex with your friend (like you apparently want to anyway) than by not having sex with him. If the friendship's depreciating either way, might as well maximally enjoy the value it still has before it tanks.
add: I suppose before expecting any 'outlier' advice to be taken seriously I should 'fess up-- almost 2 weeks ago my bf and I fooled around with a 'bi-curious' friend of ours (I called him 'heteroflexible,' because he told me months ago he's done stuff with guys before and liked it- so it sounds to me like his curiosity's satisfied and now he's just occasionally semi-gay). And our friendship's fine- he's even said he enjoyed it and would be up for it again sometime- and me and my bf's relationship is as fine as it's ever been (even though we've been a bit of a mismatch the last 7 years). We'd been flirting with him for ages and then one night we ended up play-wrestling followed by supper, a bit of friendly massage, and then ho-boy... So I'm not talking total abstractions out my ass. It can work out just fine. It's very situational and dependent on the parties involved, so don't put too much stock in advice that just assumes constant, inflexible absolutes.