Stay with her and jack it to gay porn whenever you want because sex with men and sex with women are pretty much the same thing: just sex.

That is exactly the sort of perspective people have on sex when they have only ever been with one person. Sex with men and women is only the same when you're watching it on a screen and fucking your own hand. In reality, the two are profoundly different. As is sex between any two different men or any two different women or (if you're kinky) combination thereof. Every couple has their own chemistry, their own balance of lead and follow, different techniques and physiques and quirks and sounds. Sex is every bit as nuanced as music. It's a creative, artistic act.

But yes, I was in a similar situation a very long time ago (bi man with a straight female partner in a monogamous relationship). It was the first and last time I was in a monogamous relationship. I'm not cut out for it, and I know that about myself now (mind you, I never once had an affair). That doesn't really inform your situation at all though, does it? You said this isn't something you're willing to end the relationship over, and that having an affair or opening up the relationship are both completely off the table. So how do you deal with the stress and tension? I don't know. I'm a terrible role model for dealing with stress. I'm the kind of dumbass who's first answer is usually "leave" and backup plan is "booze". If I were a therapist or something, though, I'd probably say: "find a way to connect with your local gay community and be open and honest about that part of yourself, even if you aren't able to act on it. You might find it very culturally valuable. Find ways to incorporate that part of your sexuality into your relationship with your girlfriend, to whatever extent you can. Come out of the closet to anyone who doesn't already know (that's a little biased because bisexual invisibility is totally a thing). Make friends you can connect with and talk about these issues with in-person, who you trust, who model the behavior you want to achieve in your own life."

Posting here was a good start, even though most people think you're just looking for tacit approval to have an affair. I wish you and yours the best of luck, I wish I had more to bring to the table.