Weeds in driveway, well water nearby – best herbicide?

Strap it to an old sack barrow or similar.
Yep, standard method is to just let the flame lick over the weeds on first application then when they die and dry out after three-four days, hit them again and let them burn away.

Guess I’ll be the lone voice to re-quote "Consult the genius of the place ". Those weeds will likely be there longer than you unless you sub-divide and develop.
Another thought is to plant something that chokes them out. Around here two rotations of buckwheat will eliminate poison ivy and all others, but that does involve labour. More or less than weed patrol is hard to say from the screen here.Eventually a perennial cover is planted.
Glyphosate is essential for some weeds (take that, polygonum cuspidatum!) but cites notwithstanding judicious use is advised.

Note: Salt, bleach and boiling water are not biologically benign. All three (I’m not entirely sure about the bleach) would work as indiscriminate killers of soil life, not just the weeds. Salt has a long-term effect and could leach into surrounding soil.

You don’t have to lug around a 20 pound propane tank to use a “flamethrower”. There’s a lightweight rod that attaches to a small propane canister that weighs under a pound, and is very portable. I’ve found you do have to perform repeat appllications more frequently than if you used Roundup. I have respect for Roundup’s abilities and don’t use it all that often, but my feeling is the associated hazards are exaggerated; unless you’re an agricultural worker who doesn’t pay attention to precautions, the potential for harm to you and/or the environment from several careful applications a year over a limited area is probably scant.

Clueless over here: is salt unsafe in well water?

I use boiling water on my walkway to kill weeds. We have an herb garden nearby, so I don’t want to use anything that will kill or affect them. Boiling water works fine. I don’t care if leaches into anything, or kills anything under the walkway. There are no linghering efects to worry about, and it kills down into the root (which a flamethrower might not).