Okay, in a one gallon bowl, you definately need to do complete water changes every other day due to the fact that the ammonia builds up quickly in small spaces. To help him heal, once a day is definately a good idea. When you clean his bowl be sure to use scalding hot water (not soap) and scrub down the insides and gravel really really well.
If possible, it's probably a good idea to try and find a tubberware or sterilite bin that's around 2 gallons to keep him in while he is healing. Also, if possible, you should try to go and buy a heater. A member of this site recommends this one http://www.fosterandsmithaquatics.co...57&pcatid=4057
for smallish tanks. The heater is a worthy investment because bettas are cold blooded, so they need warm and steady temperatures to stay healthy and to heal if unhealthy and because if well cared for they can live around 4-5 years.