Yep.... they can jump. Usually the shorter the fins the more air time they can achieve.
They jump for a couple of reasons... (trying to get away from their environment either because of something toxic, something threatening.... or if some cutie is near that they want to visit.)
Catxx is right on the money with the plastic wrap with holes idea if you can't find a lid.
Plastic wrap over a spawning tank is good too for maintaining the bubbles with humidity.... should you wander that far with bettas.
Good luck and have fun!