What would you do?

Approach very cautiously. Probably whistling.
This lets them know there's a nutter not far away. But he's respectful enough to do a little distraction rather than ask the same old cliched questions knowing you're in trouble !
I'd stay about ten feet away and probably ask them if they'd like a cigarette.
I'd then probably make a complimentary remark about something they're wearing.
It's kinda hard to be determined to end it all. Maybe I'm buying them time to reconsider. Maybe my complimenting is something they haven't heard in a while.
I guess I'd then ask if there was something I could do.
Maybe get them a warm drink as it's clearly going to be cold.
Maybe by this time they might consider taking me into their confidence and letting me know how they got to be where they are.

Use diversionary tactics. Talk to them. Try to engage them in simple conversation. Ask them who I can call for them-a loved one? Tell them I can listen to them for as long as they need. Try to get them to say what is bothering them. I would ask someone, if available, to go get help. Often people just need someone to listen to them and to care. Both are easy for me to do. If they jumped, I would call for help. Likely they will do serious damage jumping into shallow waters. I would be prepared to do a rescue. CPR included. And trauma nursing.

Try to talk them down.

Whip out my camera...?

I just wanna watch, I don't want to interfere with what their natural behavior would've led them to do. Honestly, it would be so annoying to me if people tried to stop me from jumping off a bridge and made a big deal out of it.

I would probably try to engage the person, but I would most likely be a bit panicky and start 'pleading' instead of reasoning.

offer him a beer and ask if he cares to tell me what's up?

I would beg them 2 not jump and talk 2 them

mind my own business.