AK, AQ, AJ flop miss

[i3betwidposition]

Everyone folds, I raise on the button with AK,AQ,AJ and SB or BB call and it's a HU situation.

The flop completely misses my hand but I bet out and SB or BB calls.

Now....

Should I bet the turn and check down the river? OR Should I check the turn and if SB or BB bet out, I call? OR Should I check the turn and if SB or BB bet out, I raise? or just fold the river?