A betta is like any other tropical fish. If you would cycle a tank for tetras/discus/danios/cichlids, cycle it for a betta.
Many places say you don't need to cycle because betta are the new goldfish - many places advocate keeping them in small spaces as a 'low maintainence' pet. True, bettas can thrive in smaller tanks than most fish but their needs are surrounded by misconceptions and myths.
I would always cycle a betta tank. However, if you can commit to all the necessary water changes, including those times when it needs to be done more than once a day, then you can go without cycling. Bettas are also considered by some hardy enough to handle a fish-in cycle, but I'd never do it. Having had to keep my bettas alive through ammonia/nitrite spikes, I wouldn't be happy to inflict that upon them intentionally.
You also wouldn't be able to leave them for more than a day or so if their tank is uncycled. A holiday would be a no-no. Cycled tanks are so much easier to maintain.