A 1st degree burn begins to heal within 3 days but for the 1st degree burn to fully heal it can take as long as 20 to 30 days for the 1st degree burn to fully heal up.
When the skin that has been burned by a 1st degree burn starts healing the skin should start peeling off which is a good sign.
It's a good idea to keep the skin clean and wrap it with Gauze while the burn is healing and if it gets worse or shows signs of infection you should see a doctor.
I would advise keeping the burn covered with gauze for at least 15 days but you can keep the burn covered until it heals.
Just be sure to replace the gauze often and clean the area to keep it from becoming infected and within 20 to 30 days the burn should be fully healed.