You can cycle with a Betta safely provided that you make the needed water changes, don't overfeed and remove uneaten food after feeding
With "fishless" cycle you need a water pram test kit to test or away to test the water daily for-ammonia, nitrite, nitrate, pH (how else will you know how much and when to add ammonia and when the cycle is complete),-cycling can take 4-8 weeks-depending on temp and pH-no water changes are needed except for one right before you add the fish and some to keep ammonia at or below 3ppm, you also need an ammonia source to add-usually on a daily basis until you see nitrite reading.
"Fish-in" cycle-you don't have to have a water test kit, however, it will make cycling easier and help you know how much and when to make water changes as well as tell you when the cycle is completed. Without a test kit you can safely cycle by making daily to every other to every 3rd day 25-50% water changes-depending on bioload, tank size, water temp, filtration and other factor for 4-8 weeks-and water changes anytime the fish behavior changes
If on city water supply a dechlorinator is needed for both cycling methods
You have to have a filter or aeration 24/7 for the nitrifying bacteria to thrive and colonize for the nitrogen cycle.
The nitrogen cycle is a process where the ammonia excreted by the fish or ammonia source is converted by a bacteria to nitrite and another bacteria convert the nitrite to nitrate-these bacteria need a stable oxygenated water flow to colonize and are limited to bioload in the tank-for example: fishless cycle for 10 fish and you only add 1 fish-the bacteria for 9 fish will die off.
The good bacteria are sticky and adhere to everything in the tank, like the walls, decorations, plants both fake and real, in the top layer of substrate and in the filter media-very little is in the water column itself so water only changes will not hurt or prolong the fish-in cycle process
You know you are cycled when water prams read:
Ammonia and nitrite 0ppm
For several days without water changes in a fish-in cycle
Care of the filter media is also needed to prevent mini-cycles/ammonia spikes-over cleaning or use of chlorinated water can kill the good bacteria-best to rinse/swish filter media in old tank water with a water change 1-2 times a month and when the water flow slows.
With all this said....if you plan on a tank without a filter or smaller than 4g-cycling is moot-due to the needed water changes that are required to keep the water quality at safe levels for the Betta health and fins.
If you have the time and dedication to make the needed water changes, "fish-in" cycling can be safe and easy, if you don't have time or dedicated to the wet-pet-get a test kit and cycle "fishless"....