If you have ever put a betta fish in a 20-gallon breeder tank (or perhaps larger) than monitor the betta's swim pattern by measuring its distance swam before it pauses. I found that a betta fish will swim close to half the length of a 20-gal breeder tank before it pauses briefly and continues swimming again at about this same distance every time. Which makes a 10-gal aquarium the ideal size in length for a betta fish. Now, this probably seems like it's a very roomy tank for a betta, but you can try adding a few smaller fish into this setup as well because let's not forget that a 10-gal tank also has width and height to it.
Betta's I would say are close to 2 inches in length at adult size, which means you may be able to get away with adding several neon tetra's which are about 1-inch in length (be sure to do research on tank mates for your betta because they don't get along well with numerous types of other fish such as other betta fish, guppies, goldfish, etc.). There may be some exceptions to this rule of tank mates, but I prefer not to risk it as it can cause fish injury, death, or having to return tank mates. An aquarium should be fairly stress-free for all its inhabitants.
You should be able to find a 10-gallon aquarium for a mere $10 in-store at Petco (they have a $1 per gallon sale about twice a year and I found select Petco's may always carry the 10-gal's for $10), and it's money well spent for a healthy betta fish habitat. You can also find inexpensive secondhand aquariums from Craigslist, LetGo, local antique shops, and sometimes even yard sales. In terms of cost for aquariums, I generally stick with the $1 per gallon rule, and no more than $4 per gallon for larger used aquariums (if the aquarium has a lid, etc. than obviously, the cost will be a bit more).