Order
Mundungus showed up to the fight very late, probably around the same time Dumbledore showed up, or maybe a minute later. He received Abe's patronus right after he finished buying some cauldrons at a "great price." He had to go home to stash the items before going to Hogsmede. He got Ed's patronus right before reached his house, and finally apparated to Hogsmede (in a mask and sans hat) in time to see the tail end of Dumbledore's fight with Bellatrix.
He spent the time getting the injured out of there. He probably made a few return trips to make sure he got everyone out.