I'm probably a very rare example of a bisexual (maybe also pan-sexual) man, in that I've had extremely little sexual experience with female-bodied persons -- even though I'm (these days especially) equally attracted to guys and gals / men and women. I've been in two long term partnerships with men thorough almost the entirety of my adult life. My latest partner (a man) and I have been together for nearly 30 years, to round it off. And while our relationship has been open / poly for almost this entire duration, I've not had a lasting and truly meaningful relationship outside of our pair bonding for this whole time.

I've had "dates" (so to speak) with a few women in this time, but none of these were likely to "go anywhere". (I overwhelmingly prefer only to have sexual relations with persons with whom there is a lot of mutual connection, trust and affection. And tend not to involve myself in "casual sex".)
I did have a sort of a girlfriend -- for a few weeks -- when I was much younger, but it didn't last long and my HIV status was unknown (and I knew I was
potentially infected) ... and so I never entered her flower ... though we did lots of naked cuddling and wet sloppy kissing!
And then there was the casual friend who offered me casual sex, which I took her up on. I did enter her flower, but that was with a
condom -- and it only happened just once!
I have a great longing to make love with my girlfriend without a condom!
I presented the word condom in bold and italics because this is a major concern for me at the moment. I despise condoms! I mean, it prevents actual contact where contact is wanted most! And they are tricky to use, in my opinion and experience. They can readily slide off during copulation!
Anyway, I now have a serious girlfriend -- though she lives far away at the moment. We plan to spend months in the same town (my town) soonish, and so there will almost certainly be some horizontal mambo dancing. And so I want to contemplate birth control topics and discuss them with more experienced people than myself.
I really don't want to use a condom. But I also really don't want to be a jerk or an asshole with my sweetheart. I don't want to shove birth control responsibility onto my very feminist girlfriend! -- and not only because that will land me in the doghouse if I try that maneuver. I really do love her!
I understand birth control pills ("the pill") can be a bit of a disaster for women, much of the time. I've heard that a woman will feel as if she is "always pregnant" on the pill. So I'm really not sure I want to ask her to use that method!
What are our options? What our our good options? What should I do? What makes good sense here?
I suppose one possible solution would be me having a vasectomy. But this seems a rather expensive and severe thing to do. But maybe it isn't as severe or expensive as I imagine?
I don't have medical insurance ... and it looks like the procedure would cost at least $1,000 US.
https://www.goodrx.com/conditions/birth-control/vasectomy-cost
That's a fairly large chunk of change in my world.