Being in several combats, himself, this is only a little bit new to him. He's used to fighting against other Half-Bloods, not giant, hairy, talking bears. Michael will stay back and try to find a bit of higher ground, preferably out of the reach of the bears. He then will start raining down golden shafted arrows, attempting to distract or redirect the attacks of the bears, giving his compatriots better survivability. Perhaps firing into feet or claws, or into a barrel to spray whatever's in it all over the bears. Michael will try to use the environment against the bears.
At this point, he is not one of those Tolkien Elves and their shooting while moving kind of archers. He will attempt to stay in one place. If he has to move to get a better position, he will, but he won't fire while moving.