not all bridges have fences, only the most infamous ones like Golden Gate, and it's not a normal fence that you can climb on and still jump; there is a safety net installed, like 3-5 m below bridge level, so that net would still catch you.
I think jumping from a building would be better; just make sure it is.
1) at least 30 m high (100 ft)
2) you land on concrete
3) you don't land on anybody (if there is a tunnel from someone can come—DON'T use this place); also, don't land on any property like cars
4) Be sure all the way down is clear, and there aren't any cables, nets, trees, power lines, umbrellas, antennas, or other stuff people put outside windows or on balconies. Any hit mid-air will alter your falling and will take some of that energy, which you DO NOT WANT
5) try to land on your head or at least on your torso—belly or back, not your legs—although "steering" yourself mid air is not easy. I found just leaping like you would into a water pool would be enough—you stand on your legs, and you lean forward until you lose balance and start falling.
Landing from 30 m on concrete on the head is practically 100%, on the torso is 99%, and on the legs it would be around 95%.
TIPS to overcome SI:
1) you count to 5 [you want to jump on 5] but you jump on 2 or 3—you trick your SI this way.
2) if you are on flat surface like a roof, face away and start walking backwards; if that's not enough, close your eyes and walk backwards
3) The obvious one: intoxicate yourself with benzos [ideally] or alcohol, although alcohol sometimes helps people survive because it relaxes the muscles. But 30 m on concrete wouldn't create much difference; maybe lower CTB rate by 1%. (But if you have to overcome your SI using any kind of substance, depressants or disccociatives, it is.). Some people will tell you, "oh, dont use alcohol, because alcohol makes you survive (no matter what)"—it's not true. From lower heights like 5–15 m, sure, being intoxicated by alcohol makes it better to avoid catastrophic injuries, but when the speed (height) is enough, alcohol won't alter much. And if it's the only way for you to overcome SI—for example, you can't do it sober and you don't have access to benzos—I'd advise you to still use it and don't be afraid it will botch the attempt. It won't.
Hope you could do it, although IMO jumping is one of the more extreme methods, SI is strong and its hard to push you to do it. I bungee jumped from 100m and its scary to do that step/leap even though you know you won't hit the ground...