You can pace yourself with respect to the height you’re comfortable experiencing. It forces you to learn to fall safely. Most importantly, it progressively associates a positive outcome (route completion) with height.
If it's still a problem even with a railing, safety system, etc, then I would think some sort of therapy or controlled exposure might help.
My palms still get sweaty, but mentally I have no irrational fear anymore. As long as think the harness is good, I'm okay.
I don't think it's so much that I got over the fear, just that mentally I know that the equipment has me and I'm not going to fall to my death.
I went tandem skydiving for the first time. I think I felt afraid, but I just decided to go through the motions.
As corny as it sounds, I think it's just mind over matter. Know that you're capable of doing whatever simple thing is required, and knowing that the bridge railing, safety harness, etc is going to protect you.
If you can stand on a bridge 1 foot in the air, you can stand on a bridge 1,000 feet in the air. If you can balance on a beam 1 foot off the ground, you can balance on a beam 100 feet off the ground. If you can climb a rock wall 6 feet high, you can climb a rock wall 600 feet high.
13 years and I've not been able to visit any countries that I'd love to visit. It's shit. There is no advice that can help me.
Indoor bouldering is also a great way to get started. I'd avoid anything outdoors as a beginner, also lead climbing is probably not your best bet.
I did it the other day, it was intense. The hardest part is the anticipation. Once you're stuck and experiencing it and realize there's no backing out you just let it happen. Also you're experiencing a lot more than heights so it makes it easy to get over that part. Do that a few times and you'll condition yourself. That's what I'm going to do.
I have a reasonable fear of heights. And I thought that I'd 'freeze' at the plane's doorway. No such thing. It was literally a breeze. So much so that I immediately wanted to repeat the experience.