hey =) I'm in the situation you are describing. LTR with my bf of almost 5 years, had always had little "flings" with other girls but never relationships. Until last fall when one happened to blossom by surprise into full on love and serious relationship.
I have no desire for another partner. I never did (or realized I did) until she came along. Now that I think back on it though I realize I was never fully satisfied with just sleeping with girls, I always wanted more and felt like something was missing. I think this was more an issue with my sexuality than a poly issue. I haven't been attracted to any other men since I started dating my bf. I'm just not interested in them. I needed a relationship with a woman, the connection is *so* much different between two girls, and it suits me perfectly.
I've always identified as bisexual but I don't think I'll ever identify as poly. I struggle with the idea of it and even at the beginning was scared I was getting in over my head. I have a hard time with the idea of how being in two relationships will pan out (as this will always be a V, never a triad, gf is a lesbian.) I have a hard time picturing it working in aspects like living together, having a family, marriage etc. I feel so connected to both of them and want them both to be "primaries" if you will. Maybe it's something that gets easier over time. Maybe I have some things I'm unwilling to admit to myself. I guess just be ready for a lot of self exploration.
I also have gone through stages of acceptance with my lovers being with other girls. First couple yrs I was w bf - no way I would let him be with someone else. After a while I let him watch me and another girl, then let him join a little bit, then we had sex with another girl together, then I was okay with him being with her without me around and taking her out on dates. Things pushed past my limits then because of issues on her part and things came crashing down... Kind of hurt me and I let go a bit, all while my new relationship with gf grew. Now I am feeling much less possessive of him. I encourage him to flirt and pursue things with other girls. I guess I just want him to be satisfied because I fear I can't give him everything he needs...and I don't want to lose him in my life. I don't get very jealous because he makes me feel secure in his love for me and I also have gf to keep me confident that I'm desired. Gf on the other hand we've been dating less than a year so I am keeping her very close to me. It takes time to build trust. I'm extremely passionate about her too so I get more jealous thinking about her with someone else. I can see us being with another girl together (sexually) some day but not until I feel more secure. I don't think I'd ever be okay with her being involved romantically with someone else though out of fear of her leaving me.
As for finding a gf, if things go for you anything like they did for me, I found her when I stopped looking (I know, so cliche lolol.) Be honest with her and yourself and find one with an open mind. Take some girls out, make them feel special and let things happen naturally. Good luck.