Backpack getting a little too heavy? Starting your own legendary shop? Well you’re going to need somewhere to store your rainy day legendaries, can’t be carrying all that precious cargo around on your main, now can you? Well make a mule! Just create a new character, load a co-op game with both your main character and your new level 1 character and give the level 1 the items you want to store. It’s as simple as that. If you want a really epic bank, you might want to get some more slots by rescuing claptraps.
Update: Make sure to heed RedBeardRaven’s advice from the comments:
I think it should be noted that you have to have a new profile loaded to be able to be the mule. You do not have to have xbox live gold for this to work properly, but if you want to trade from your mule directly it could make it easier. Also, do not just open a new character without a profile loaded, or else the loot that you transfer over will be lost after you end the game.