This might be a repeat of what some of the others have said--but normally bettas don't like to have the air stone on full blast, especially if it is a large one. At times when I have to use them, usually when dealing with anitibiotics or fish with swim bladder problems, I use a gang valve--if you don't have one, you can simply tie the airline tubing into knots or crimp it, then fasten it with a binder clip.
Is the bamboo live? Many pet stores market non-aquatic plants as if they were aquatic, however these bog plants cannot live with their leaves submerged and will rot in your tank. Other live plants like java fern, anubias, java moss, and hornwort are easy to care for true aquatic plants that make great additions to a low-light tank. These will improve the water quality and provide your betta with more environmental enrichment.
Also be aware that if they are real rocks not intended for aquarium use, it may leech minerals into the tank, creating very hard water--so be very careful if you choose natural rock for your aquarium.
It's normal for bettas to be picky eaters when you bring them home--depending on the store, many get fed live or frozen foods before you buy them. Sometimes they've never seen a pellet before, and sometimes they're a bit bratty. Wardley betta pellets are not very high quality, and freeze dried foods are not very nutritious and are very difficult for bettas to digest. I would switch him over to a high quality pellet food, OmegaOne Betta Buffet Pellets, Atison's betta pellets, Ken's betta crumbles, and New Life Spectrum are all very good brands. Soaking the pellet in a little tank water will help release the "scent" of the food, and make it much easier to digest.
Personally, after my experience with freeze dried foods I'll never give them to another betta. One of my halfmoons became so constipated from them he didn't poop for a week. Frozen foods are much easier to digest and less nutrients are lost through the freezing process than the freeze-drying process. Frozen brine shrimp and daphnia are a great source of fiber and nutrients for your betta, I use these foods instead of blanched peas or a fasting period to keep my fish regular.
"Cycled tank" refers to the nitrogen cycle--the process by which your tank is colonized beneficial bacteria that consume the ammonia that fish constantly excrete through their gills (kind of like the fish version of urine). Ammonia is toxic, and can make your fish very ill--you do large (both 50% and 100%, cleaning out everything with hot water during 100% changes) water changes on an uncycled tank in order to keep this ammonia in check.
In a cycled tank, this ammonia is converted into nitrite, which is also poisonous, but there is another bacteria that converts this into nitrate, which is much less poisonous. You still must do some water changes in order to remove excessive nitrate, but much less than you would if it were ammonia or nitrite--I do 30% changes once a week on my cycled 10 gallon. Much less maintenance.
Whether you cycle the tank or not, you should purchase a liquid master test kit so that you can be sure that your water changing routine is taking care of all of the ammonia. When/if you do cycle, you will have to have this kit to help you do it. I am also an advocate of fishless cycling--though I prefer to keep my fish in plastic rubbermaid/sterilite storage bins as temporary housing--4 gallon ones are only about $3. Very economical.
It's a good idea to research the nitrogen cycle as well as different methods of cycling. If you want to buy more supplies--such as a filter, more dechlorinator, test kit, food, medication, plant supplements--whatever, I suggest shopping at this site: http://www.fosterandsmithaquatics.com
they offer a great variety of supplies at much lower prices ($10-$20 lower) than any pet store I've seen--if you order just a couple of items you've saved enough to more than make up for shipping.