Pardon me for interjecting, but is stocking the tank when it's not fully cycled yet a good idea? Or am I just misunderstanding?
Not a problem interjecting. Getting questions answered is how we learn.
Let me start by asking a different question: "What does 'fully' cycled mean?"
The answer to that is the answer to your question. "Fully cycled" simply means that the FULL amount of ammonia produced by the fish can be processed by the tank. A tank that can fully cycle 1 ppm in 24 hours can't handle the same bioload as a tank that can process 3 ppm in 24 hours, but it can handle approximately 1/3 that load.
A tank that can cycle through 1 ppm in 12 hours can handle approximately 2/3 of the load of a tank that can handle 3 ppm in 24 hours.
No tank is ever 'fully cycled' to its maximum. You can always add more fish, increasing the bioload, and the tank would have to increase its bacteria colony to compensate. But, there's a limit to how many fish you should stock in a given tank, and we use the 3ppm dose to replicate that. But, if over the years, the fish die off and you end up with 1/10th of the original group of fish, then your tank is no longer 'fully cycled' for a 3ppm bioload. You would need to slowly increase the stocking back up, or... pull the remaining fish out (and house them temporarily elsewhere) and 'recycle' the tank... growing the bacterial colony back up to the necessary size.
So, what I was suggesting was that because there are plants, they are potentially going to be damaged by the ammonia, it would be prudent to limit the ammonia in the cycle, and then stock slightly more slowly. Its not a big deal, and it will lead to the same result... a fully stocked planted tank. This method has worked for me several times in the past. And it doesn't take long to get the full stocking after the initial cycle is completed. Once the colony is going, it can grow fairly quickly to deal with an increase in bio-load... under optimal conditions these bacteria will double roughly every 12-24 hours. So, it won't take long to get there once its started.
EDIT: I forgot this is a single betta tank. Getting the tank to handle 1 ppm every 24 or 12 hours will be sufficient. The bioload of the betta isn't nearly that much compared to a 'fully' stocked tank.