What to do with blood blister after burn? What can I do so it doesn't get bigger?

Shouldn't get bigger. But a blood blister after a burn is serious enough you should have it looked at.
Cool compresses. Apply cool compresses to the area a few times per day. If it continues to enlarge, you can pop the blister with a sterile needle, but do not remove the blister skin as it acts like a dressing and protects the skin below it.