Yes, it is normal. Many bettas are hide and refuse food while they adjust to their new surroundings. Keep in mind that whenever you feed your betta dry food of any kind, especially freeze-dried food, that it should be fully rehydrated in a bit of tank water before feeding. Bettas are very prone to bloating and constipation as a species, so it's best to avoid it in any way possible. If you think about it, fish were not designed to eat dry, bready, air-filled foods. What they go through after they consume them is analogous to when we eat uncooked rice or noodles. The food takes on moisture and expands in the gut--causing bloating, discomfort, and constipation, especially in freeze-dried foods. I prefer to use a mixture of different pellet brands and frozen foods instead of freeze-dried because they are more nutritious and fully hydrated. For bettas, variety is important since one single pellet brand cannot provide your fish with complete nutrition. High quality pellet brands you should consider include OmegaOne betta buffet pellets, Atison's betta pellets, and New Life Spectrum.
When you say you let the tank cycle for a day, it does not mean that your tank is "cycled," as we would say it. All you did was simply run water through your filter. When we say cycle, we mean the Nitrogen Cycle. This is the process by which beneficial bacteria that live in mature filters consume the toxic ammonia your fish excretes through its gills constantly as waste (kind of like the fish form of urine), and converts it into an equally toxic substance called nitrite. Nitrite is then converted by more beneficial bacteria into a much less toxic substance called nitrate. Once your filter has been colonized by beneficial bacteria (cultivating a colony takes about 3 weeks), you will only have to worry about controlling nitrate with partial water changes, rather than working yourself to death trying to maintain a 0ppm reading of ammonia (which would take 100% water changes to maintain.)
I highly recommend researching the Nitrogen Cycle and learning how to cultivate a bacterial colony in your filter safely. You will need to purchase a liquid master test kit, like this one: http://www.fosterandsmithaquatics.com/product/prod_display.cfm?c=3578+4345+4454&pcatid=4454
in order to complete the process and keep your fish safe while the ammonia and nitrite spike during the bacteria growth stage. Test kits are a great investment, just do not buy the dip strip version--they are a rip off. Very expensive per test compared to liquid and not nearly as accurate.
Until the tank is really
cycled, you will have to rely on your testing equipment to know when to change the water. Your goal for the moment will be to keep the ammonia reading at or below .25ppm so that the bacteria have enough ammonia to feed on and grow, but there is not enough to poison your fish.