My son uses a Mizuno MX equipment bag. ( NOT A CATCHERS BAG ) $100 bucks but holds everything ...
4 bats,catchers equipment w/mask,cheats,reg glove,batting helmet and a change of clothes for practice.
It has wheels and they have held up good ... the handle is great with a 2 post slide system.
You are able to lock it with a small combo lock ( made 3 trips to PG events and held up thru air port )