Should you cover blister with a bandage?

yes, but first you want to clean it so as not to infect it. Get a cottonball or cotton swab (Qtip) and dip it in some alcohol (not the drinking kind, of course), then rub it on the blister. If you don't know, it will sting, but it's killing any germs on the cuts. Then put on the bandage, not the Band-Aid kind that has adhesive. You want the kind you wrap around.
If you have something like neosporin, you could use that instead of alcohol.