Bacteria blooms are common on new tanks. I wouldn't worry about that at this point. Anything new should have been thoroughly rinsed in hot tap water before you added it through.. you did that right?
Ammoia poisoning is from lack of water changes, not over changing. Changing the water is the only way to remove ammonia.
What is the temperature of their tanks? It should be a stable (unchanging) temp between 78-80F, and you should use an in tank thermometer to monitor it.
The .25ppm ammonia is also a problem.. A lot of people will say you can't cycle a tank of this size and it will always require twice weekly changes of 50% and 100%, but you can try.. best case scenario is it will always need twice weekly 50% changes using a small siphon or turkey baster to remove poop and debris from the gravel.
To cycle, you should ideally usa reliable drops kit for ammonia, nitrite and nitrate. You should be testing daily for ammonia and nitrite and doing an extra (in addition to a weekly 50% change you should always do) change of 50% any time you see as little as .25ppm of either. At first you will see ammonia spike, then nitrite will spike. Eventually, even after a week of no water changes, you will be left with no ammonia, and finally nitrite will follow. At this point you will be left with only nitrates. These should always be kept <20ppm and the lower the better. At this point a twice weekly 50% change with siphon/baster may maintain water quality. Be aware cycling can take up to two weeks and in something so small it may take even longer or it may never fully establish: http://www.bettafish.com/showthread.php?t=47838
Also the filter you have has an unfortunate flaw. It only has one type of filter media (one cartridge) which needs to be changed monthly. However, that is where your beneficial bacteria grows, so every time you replace it you restart your cycle. I suggest removing the cartridge and instead stuffing it with 2 filter sponges.. you'll just have to look around to where you can find somethings that will fit, or cut them to size. These you only need to replace once a year, and if you replace them a month a part it should not hurt your cycle. Also putting a very porous sponge around the intake of the filter will keep your betta's fins from being hurt, and provide an additional place for the bacteria to grow. You can attach it using a silicon band or even rubber band. All these sponges should be swished in the old tank water after a water change at a couple times a month to keep from getting clogged.
Also water changes should always be done with same temp water (use in tank thermometer to match running tap to current tank temp) and premix with conditioner before being added to the tank. If you don't already have something you are premixing water in, you can get some gallon water jugs from the grocery store - rinse thoroughly in hot water, never chems.
Hope this helps..