There's a big red button on the back of each bumper, and hitting it will cause that bumper to shoot off with much more force than usual. You can use this to chase characters down and push them off the edge, though it's difficult to catch up with them, since you move at the same speed. Instead, it's best to get behind characters while they're locking horns with another, so you can sneak in and push them off quietly.
Centre stage
Where is it going to be safest? Erm, well, the centre of the stage, right? Exactly, it makes perfect sense. At least, from a defensive standpoint. Being in the centre in Bumper.io is a bit like hiding in buildings for the entire game in PUBG. Yes, it's possible, and a decent strategy to win, but doesn't make for the most intense gameplay experience. At all. Moving away from the centre is best for offense, but of course can leave you vulnerable. Though, if in the final moments you're going against a larger enemy than you, you won't likely last long.
Pull up to me bumper
So Bumper.io is about wee round bumpers that look an awful lot like the robots in Nier Automata, all bumping into one another, trying to know each other off the edge of a ledge. And the stages you battle on are what make the big difference here. They go from wide squares, to far more narrow platforms that you'll have to navigate. Your knowledge of the stage layout will be imperative to your victories. They're random, so just try to memorise them as they come.
Size matters
Bigger is better, right? Exactly, and that's why having a larger character, with more weight and grunt, will fare better against these wee bumpers. Luckily, each time you push someone off you get a size increase, making it even easier to push others off. Nice. Beware though, even when you're larger than life, it won't matter if you're being pushed off the edge by multiple opponents.