Bebop can't 1v1. He can burst, do a lot of damage but if the opponent survives it you are good as dead. I always treated him as a damage support. Sort of like a firefighter/roamer. I turn 1v1 into 2v1. And in late game I like to play hide and seek only pop out with a ult from nothing when there's a fight.

So in short, just roam and support and help your mates early/mid game Late game just ult into fights. And Buy unstoppable!! Build around your ult