Shen can crap on him in lane just by trolling his barrels on last hit, as well as ruin his ulti to protect your squishies. Early ganks help to delay the eventual scaling into being nuts with damage, a bronze gangplank will run out of mana fast trying to last hit, so taking Pantheon and harassing him with your spear every time he walks up (and they will telegraph it) to Q a minion for extra gold. Using a pick that can poke him down and force him to spam W for heals works too, make him CS under tower, most bronze players cant CS well and he will almost pray to god he can barrel correctly if you poke him down, waste his mana and force him under tower. You can do this with Jayce and Fiora since theyre just as bad to deal with as he is with more reliable damage.
If he is fed or just has items to be trouble later in the game, do not force fights or fight at all in small quarters of the map, get him in an open area, make him work to set up those barrels and get himself in danger. Like for me, im mostly playing Lee and Elise, if i can land that cocoon to make him waste his W, its on and he's dead, barrel or not. I also like to flash kick GP away from his barrels and into my team with Lee. His damage mostly comes from barrels and if you can stop them, you can shut down GP in Bronze pretty damn hard. As a support main, try taking something that can make him panic flash or use his W too soon so you can shit on his barrels easier or just flat out kill him, like a Thresh pick or a Bard.
My absolute favorite to mess with a GP in bronze, is maxing E on Nasus, not worrying about your stacks and going full tank. He walks up to CS with Q? drop your E on him, he tries to Q you? Drop the W and E, make him waste his W and keep harassing him. Dorans Ring and biscuits with 0/18/12 as masteries, Thunderlords or Stormraiders either is good, make sure to take bandit, meditation and runic armor. Give him the Quas dicking.
GP is really easy to deal with at any point of the game in bronze once you figure out he sucks with no barrel pressure.