I guess what you will do is going to depend on how much you value your relationship with your girlfriend. There's no need to deny that you're bisexual but there's no real difference between you hankering for some male bonding, than a straight guy wanting to know what it's like to be with another woman. Granted, your GF can't offer you what other men can so that may be a point to work on to some extent.
If your girlfriend means the world to you, then it's worth seeing how open-minded she is about sexual matters. Take some time to explore sexual fantasies with her and you never know your luck. She may (like quite a few women) enjoy the idea of you playing with another guy. If however it's obvious that she finds the idea of male bisexuality a turn-off, then you need to focus on your current relationship and consider other ways of exploring bisexuality that won't affect your relationship. Perhaps your GF may be open to playing with strap-ons or watching porn that has a bisexual theme to it.
If your relationship isn't one that you feel is going to work out for the long term, then your need for bisexual fun is probably going to be just one other factor that leads to you breaking up. I don't recommend doing anything behind her back but if you think that you'd ultimately prefer to meet a woman who is open to your bisexual leanings, then you'd best be honest with your GF and play as a free agent.
If (another if!), you do decide to pursue something behind your GF's back then needless to say, ensure that your bisexual sex is completely safe. Condoms all the way.