The bigger the aquarium, the easier.
I firmly believe 5g to be a minimum for a betta, anything less, as you're seeing, is such a bother and is stressful for the fish to constantly be removed from their home for cleanings.
A planted 5g with some MTS or pond snails and your can just change out a gallon to two a week and be fine. With two, do the same but in a divided 10g (with 2-4 gallons a week).
Plants make everything better (and note the plural on plants, one will not due).
In a 5 gallon, with no live plants, 40-50% weekly with siphoning is the recommended amount.. with live plants, depending upon type and how many, 30% is the average per week.
It all depends on the amount of live plants (if any).. but a 5 gallon and a 10 gallon is the same with no live plants (at 40-50% per week), and live plants will lower it the same, depending upon how many you have.
Adding snails in the mix, whether it be live planted or non live planted, you will up your water change %, depending on how many snails- the more snails you have, the more you will have to change as they create a very large bio load.
And whenever doing a 40-50% water change, on any size aquarium, it is always safer to remove the fish.
Now, in an established tank that has a certain amount of live plants, shrimps, etc you can get away with even less... but it has to be almost packed full of plants.