Bettas are tropical fish, this means they need temperatures of 78-83 degrees to be comfortable, healthy, and active. Just a few degrees doesn't seem like it would make much different to big warm-blooded mammals like us, but to a 2" cold-blooded fish, it's the difference between regular and constipated; active and lethargic. I highly recommend returning the bowl and getting a larger container that can be safely heated.
Most heaters are designed to be used in containers of at least two gallons. I only recommend 25watt adjustable heaters, such as this one: http://www.fosterandsmithaquatics.co...m?pcatid=11368
because non adjustable heaters have no thermostat and won't heat your water enough, may overheat it, and will allow the temperature in the tank to fluctuate dangerously. Adjustable heaters are a much better investment that will pay off in the health and longevity of your fish.
Please keep in mind that a 1 gallon container must have a 100% water change and cleaning every other day in order to control the ammonia that your fish is constantly excreting into the tank. Ammonia is a highly toxic substance, in nature it would be converted into less toxic compounds by specialized bacteria, consumed by plants, and diluted by larger quantities of water. In small containers like this one, you have to do the job of all three of these elements--and that takes work. Make sure you condition the water with a dechlorinator with each water change and carefully match the temperature of the old and new water before you begin acclimating your fish.
As for feeding, which I forgot is the actual topic of this thread, you should try to get a quality pellet and use that as a staple, and supplement that with the frozen foods. I recommend OmegaOne Betta Buffet Pellets, Atison's Betta Pellets, Ken's Betta Crumbles, and New Life Spectrum. All of these are good brands.