I don't know where this myth that small tanks don't cycle came from... All tanks will establish a nitrogen cycle provided there is enough surface area for the bacteria to grow on, that's where the bio wheel comes in, although for a small bioload like a single betta, gravel, filter media, and decoration surfaces are probably more than sufficient. You do not need to add a source of bacteria for this to happen, the bacteria will get into your tank from the world at large unless you live in a sterile bubble or something. However, adding a source of bacteria, like filter media from an established tank, can lower your establishment time significantly. Don't bother with non-refrigerated bottled "bacteria", they don't really work. The refrigerated kind like Bio-spira does work somewhat, but gravel or media from an established tank is better and is usually free.
You can fishless cycle the tank with ammonia before you add the betta if you like. There have been quite a few posts about it lately in the beginner's section if you are interested in the method, i'm kinda tired of typing out the same instructions over and over.
Fishless cycling is very humane in that it prevents your fish from coming in contact with toxic levels of ammonia and nitrite which can cause permanent damage or death. It does require a lot of patience on your part, but that's a good trait to nuture in yourself, especially as it relates to fishkeeping.
Now, bettas are generally pretty hardy and can make it through a small tank's cycle establishment period most of the time. The fact that they breathe atmospheric air can compensate for any long term gill damage they may sustain from toxic levels of cycle biproducts. If the betta is weak (as many pet store bettas are), elevated ammonia and nitrite may further weaken the fish's immune system and cause it to display symptoms of disease. If you choose to cycle with the fish in the tank, you should test the water every day and will probably need to perform small daily water changes (20%) until the cycle establishes. I don't recommend the 100% weekly change, as the betta will be living in 6 days worth of metabolites, then you'll do a full change and remove the products the bacteria are feeding on, retarding the growth of the colony.