having and boyfriend and dealing with bisexuality

Hello,

I've been wondering if you can help me with my problem. I really need to get it of my chest.
I'm 22 and I'm with my boyfriend for 2 1/2 years now. I already knew before I met him that I was bisexual as I was madly in love with a girl for about 3 years. She didn't want to be with me although we always did things which I suppose friends don't do (hugging for ages, groping around when we were drunk) but she always told me she didn't remember in the end so I think maybe she denied it or whatever. So we never had actual intercourse but I really liked being with her and I also wanted her physically. This was probably the time when I really realised I was bi although I had known it before. I just didn't know a word for it. Actually it doesn't matter and I'm straying from the topic. So when I met my boyfriend I was just over her and I was ready to start a relationship with someone. I had thought long and hard if I wanted my first serious relationship with a guy or with a girl as I knew that I was bi. I decided to stay open minded but tended more to guys. I imagined my closer future with a guy and I just started enjoying my life a bit more. Not in terms of sexual relationships but just in terms of being me and doing what I wanted. I didn't think it would happen that soon but after a few weeks after I had pondered about my relationship future I met him. He is a lovely, cute and intelligent guy and we had an immediate chemistry. He was head over heels for me. I was very confused in the beginning because I got to know him in a foreign country and it was very complicated for us to meet up and to be together. We managed anyway and we both put our energy in being together and making the relationship work. It was like building a real environnement for us where we could be comfortable with each other.
So when we got together I still had these thoughts about me being bisexual in my mind. I was very confused because obviously I had never really acted on this feelings as in having sex with a girl. Before him I never had sex with anyone. I was so scared to tell him that I had had crushes on and desires for girls and boys in the past. Everything that was connected in my brain with being with a girl was sort of connected with that one girl that had hurt me so much. So I thought maybe it was just about her which of course was not true.
I tried to come out to him but I was stuttering around and I didn't pass the message over quite right. He thought that I just had a crush on a girl once and that it was like a "phase". I get that it is hard for heterosexual men to understand bisexuality but this really made it hard for me. He is, like I said, a very good guy but his views are sometimes very conservative. He would start talking about lesbians and gays like they are lesser people and just have a problem with their brain. I grew up in conservative surroundings as well so I already knew these kind of talks but it hurt me so much because he was the first person I actually came out to.
I think now he understands me better, we had quite a few talks about it. What I didn't tell him is that I'm longing to be with a woman in some kind of way just to make sense out of all of this. I even think about splitting up with him sometimes because I feel like all of this has grown over me. I'm tired and sick of it and I just can't continue anymore. Sometimes I'm so sad I just need to cry. I met a bisexual girl who's in a relationship a few months ago and I shared my thoughts with her and she told me that she's been through exactly the same as I am and the only solution is splitting up and going after my desires. Honestly, I can't do that. I love him so much, we've been through so much together and I don't want to throw away all of this for an uncertain future with some probably random hook ups. We are living together now for 2 months and everytime he comes home he's so happy and he smiles and honestly he did so much to be able to live with me. And I'm just having these thoughts about making out with a girl. I can't continue like this. I want to work on our relationship without having these thoughts in my mind as there are other things we need to work on. I don't want to be looking for a reason to "excuse" myself to be with a girl. It makes me so crazy you can't imagine. I just want all of this to end and I want some sense coming into my life again. I wish I could talk to him openly about it, he can't look inside my brain and see the struggle so I would just need to tell him. But I can't because I know that it is probably out of his understanding.
I don't want to end it either, I still desire him (also as a man). I just feel so dirty and shabby I really don't know what to do anymore. Has anyone of you ever been in a similar kind of situation? I would be so glad if you could answer! Thank you