BioSpira for small betta tanks - sure if you want to throw your money away??? Use that stuff on tanks with REAL loads, not on 1 fish in a small tank/bowl!
I agree, 5gal + tanks should be cycled (fishless if possible), but nothing smaller then that. People will start thinking they can get away with fewer water changes in smaller tanks if they believe it is 'cycled', which will lead to more bad water issues than if they just do regular water changes and cleaning.
Yes, bettas have gills and are just as suceptable to ammonia burns, but not as affected by higher nitrite levels compaired to non-labyrinth fish. This is not just me talking, but also the local betta breeders opinions. I did not mean to imply that bettas are not affected by nitrites, just not as likely to die from the occaisional rise in nitrites than say... a neon tetra.
The 50% water change every 3 days is also a really good idea for anything under 2 gallons. I did 33% weekly (7 day) water changes on my 2 and 3 gallon divided tanks with no issues of water quality.
Bettas can live in smaller tanks for a long, long time. The oldest betta I know lives in a 1 gallon bowl and he is 5 years old. He gets weekly full water changes and bowl rising/cleaning and thats it.
I personally think that smaller tanks are just more work than bigger divided tanks, that is why I have 5 bettas in my 17 gal (will hold up to 6 bettas). Water changes, filtration, lighting and heating are all shared, so less cords, consitant heat, fully cycled and slowly filtered - perfect for a bunch of bettas
Don't bother trying to create and maintain a bio-filter system in such a small space. Just keep it clean, sanitize it if it gets grubby, and your betta(s) will be just fine!