A 1 gallon tank is too small for a cycle to be stable in it--the ammonia would build up too fast with not enough water to dilute it--one gallons are also too small to have a proper filter that doesn't have too much flow. You and your betta will be better off with water changes every other day. I really don't recommend one gallon containers because they don't provide the betta with adequate space to excercise or provide any environmental enrichment. They are also too small to heat with a quality heater. Even if the water is pristine, these containers are too small to be suitable permanent homes.
The smallest tank I've maintained a cycle in was 2.5G--and that was with a lot of very porous gravel and a ton of java moss. The filter also had a lot of extra filter floss in it--I took the biowheel out of it and filled the outlet area with ceramic rings, and topped it with a few layers of 50 micron filter sponge. It helped buffer the flow and added more surfaces for the bacteria to colonize.
Last edited by Adastra; 07-24-2010 at 06:47 PM.