The bacteria that starts the cycle is in the air (type that eats ammonia).
I did a cycle with some Jungle Start Up bacteria and it cycled in a couple of weeks using the shrimp method to create ammonia in a 2.5 gal. I didn't take the shrimp out and let the cycle go over board on nitrate levels thus it started growing a fungus that is really hard to get rid of. Mainly I was just doing it to get use to reading water testing colors again which it did great at. After a complete clean up it will later become my hospital tank.
Farther reading told me that these non-refrigerated bacteria in a bottle you can buy are not the right kind of nitrifying bacteria you get in a normal cycled tank, though they do come in handy if you do something to a regular cycled tank to help out while the right kind of bacteria play catch up and multiply again (over feed or adding more fish than the cycle can handle). If you cycle with these bottle products and forget to add them with a water change you will have a spike and I didn't like the ideal of constantly having to add them with every water change. They are called Heterotrophic bacteria. True nitrifying bacteria can be bought in a bottle that has to be refrigerated and it will have a short shelf life along with being more expensive.
I read that both the shrimp and food methods can both lead to Saprolegnia (Fungus) getting started due to it rotting. I am now cycling a 5 gal tank using the food method, but that food is crushed, soaked and mushed to where it is basically a liquid so the fungus has no food to attach to and I'm also doing it the bare aquarium method so that the nitrifying bacteria get into the filter definitely instead of selecting the gravel or deco's. They can get into that later, your real cycling comes from them living in your filters bio media.
I like you hate waiting a few weeks to get the tank ready and if your concerned about his lack of exercise room then get a plastic container that will hold more water to give him more room in the mean time with doing regular water changes. Can't see them good through the plastic, but when you take them out into a glass container while changing water you can view them closely. Mine stayed in some Sterilite file containers for a while until I got some 5 gal tanks for them. They are only in 3 gallons of water since I have to change it to often until I can get the tanks cycled. Once 1 is cycled I'll use it to seed the other 3 from.
Since you test often and seem to only have one fish it would probably be pretty safe for you to do an in-tank cycle unless something might come up to where you couldn't change some of the water daily. Prime will lock up ammonia (converts the gas type that is harmful to the ion type which isn't-they convert back & forth depending on pH, etc.) and nitrites, but only for 24-48 hours. So using it for that is only a temp fix until you can do a water change in a non-cycled or one not fully cycled tank. Can also be used in a cycled tank to lock it up to help out until the nitrifying bacteria &/or plants can catch up with the load, but again the lock up only works for 24-48 hours. You will still get a high total ammonia reading (total ammonia=gas+ion types), but the gas type will be changed to the ion type which won't hurt the fish. I'm guessing the nitrate/etc. reading will be the same way, show up but still be locked up.
If you only have one betta, put a mirror to where it can see itself thus show off and try to fight itself which exercises it's fins and helps keep it healthy. Only do it a few minutes, so they don't over exercise or loose interest (reason store betta's rarely pay mind to each other) every day or when you get around to it.
If they get stressed cover the tank so it will be dark and they will feel safer. As for netting, a way around that is to scoop them up in a cup or container with the flow of water drawing them into it and then pour out some of the water back into the tank. Mine come up to the container checking it out and then I dip in down sideways to get them scooped in it.
Another tip I found along the way was about buying Seachems Matrix Bio-Media. If your filter doesn't have a location for it, it can be put into a medicine bottle with small holes drilled into it cleaned off to where the betta won't tear it's fins on the wholes. This gives the nitrifying bacteria a place to live and a backup to their locations in the filter or gravel. Also if you start another tank it is easy to move them.
It also comes in handy to keep your Mini-Cycle going in a non-filtered tank by keeping them in a bottle or just using it in the bottom of the tank. Since I have 3 more tanks to cycle after the 5 gallon makes it I'm going to not only be putting the filters from those tank into this one for a week before I start their cycles I'll also have some of this to use to seed the tanks and have as backups in the cycled tanks. Will also use it in my hospital tank when only salt is being used, but will take it out if other medication is used since that will kill the bacteria.