To make it clear, you can say the following: 1a. Verbally bashing others has become his habit . 1b. Bashing others verbally has become his habit. 2a. Physically bashing others has become his habit. 2b. Bashing others physically has become his habit.

"Bashing others has become his habit," or "Bashing other people has become his habit." It's not clear what you mean by "bashing". Do you mean physical assault, or harsh criticism? You need to be clear on which, otherwise someone may call the police. ;)

Yep it's correct, you just need "s" in otherS :)