I would definitely try to resolve this before you are committed (even two years is a fair amount of committment). I can relate because I am also a multi-faceted person, but the advice I can give is limited.
What makes you think you're repressing yourself? Some people claim to be 'integral bisexuals' (they need one of each), and I'm not in the position to tell them they are wrong, but just because you are bisexual doesn't mean you are giving too much up. Monosexuals give up a lot when they marry. They make a committment to one person, and they probably look at all the people they can't be with and feel similarly. So ask yourself if you actually feel repressed, or if it's just a compulsion you would be happier not giving into.
I second Martin, this isn't cause to be ashamed or afraid. Personally, I have a hard time having an attraction and not feeling bound by it. In past years, I swear I almost changed my facebook status because I saw an attractive person. But it's just a stupid attraction. Attractions happen for any number of reasons, and most of them probably aren't worth pursuing. You might have cheated on your girlfriend and found out it was the most boring thing you've ever done, and you only did it because he looked attractive.
And about cheating, it probably won't matter to her that it's a guy. Cheating is cheating, according to all the girls I've heard about who are in your situation.
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