Head for the Bandit camp to the Southwest of Tiny Tina's Workshop. This will lead you to Buzzard Academy. This is a massive Bandit camp and you can find the Badonkadonks here. Head toward the buildings and go up the stairs. Head over to the right across the walkway and then continue to the right. There you will find more Bandits to deal with. Continue toward the entrance. Go underneath the overhang below the Buzzard platform. There you will find the first Badonkadonk.
The second is very close by. Head on up the nearby stairs and turn to the left. Drop down to the ground and go forward. The second Badonkadonk sits to the right in this area. Just grab it and you are good to return to Tiny Tina's Workshop