You can chop earth worms if necessary and feed them to your axie at that size. The pieces should be no longer than the axies head is wide (although some axies have no trouble with much larger pieces.)
As long as the bait shop worms don't have chemicals, they should be fine. You can google different brands - some state that their bait worms are safe for pets.
You can dig your own earth worms, but only where chemicals (weed killer, insecticide, etc.) haven't been used.
I recommend you avoid the red wigglers since many axies don't like them (they stink and taste bad).