Busing through, slang, not sure if it is used much, but... busting through the door is an example but correct way is bursting through, same thing, bursting through the door etc. Hope it helps

Busting through, is to go through something with force. It is slightly different from 'bursting through'. You can burst through an open or closed door, but you can only bust through a closed door. Bust- to break/force open/force through and another usage of bust is to escape or to help someone escape.. ie He bust open the chest. He busted his way through the crowd. The police busted down the door. They busted him out of prison. I would not consider 'bust' slang just simple casual language.

"busting through " = a slang term = to emerge, enter suddenly and forcefully Example: The angry customer came busting through the door and asked to speak to the store manager. The police officer bust through the door when they arrived at house where the criminal is hiding in.

"busting through " = a slang term = to emerge suddenly and forcefully Example: The police came busting [bursting] through the door and captured the criminal.

bursting + through If you know what those two words mean, then they mean the same when put together.