If what your ideal is would be three of more people all together in a loving, open, honest relationship, then I think that would describe pretty much what most people see as polyamory.
But if I were you I really wouldn't get too hung up on labels - I don't really think it matters whether you are straight/gay/bi or poly/mono - the most important thing is that you (and she) work out what relationship configuration is your goal, and how it should work, then try it.
Labels are useful to describe, but can get in the way horribly - especially if you have to ask yourself "would a bi person do this?" or "would a poly person do this?"
There's some great reading on this forum and check out the excellent articles at http://www.xeromag.com/fvpoly.html
So welcome to the forum!