Bettas do not need air pump, they breath air. They don´t need filter per se but regular cleaning of the tank. 32 oz of water is perhaps too small, a small 1 gal tank is enough, some gravel and a few plastic plants to make the tank look nicer would be OK. Since bettas are tropical fish they need heat and even though a 1 gal tank is too small to have a heater placing the tank in a draft free warm place is usually enough.

I sure you will enjoy your new pet. Mine is very friendly and comes over to the side of the bowl and wags his tail! I have had one on and off for years. You can usually pick up aquarium gravel and fake plants and nets at garage sales and thrift stores, just to wash really well with plain water..no soap. I like the fabric plants the best, afraid he will scrape himself on those plastic ones. I use a glass container that holds almost a whole gallon. Some basic things you will need are:

1. water conditioner. Stores carry some that is just for betas
   2) food pellets for a beta. The Hikari brand are best. I bought some other brand and the pellets were too big, fish had trouble eating them. Don't use the flakes, too much ends up not eaten and dirtys the water. I usually feed 3-5 pellets twice per day.
   3) a really soft net to remove fish from bowl, they are usually white, fabric like. The green ones are too rough.

Change at about 2/3 of the water once per week, never change water completely. I always put fish in another container so I can wash/rinse gravel really good. I also let water I am going to use sit for 1 day so chemicals can disapate and to make sure water tempature is the same as the water in the bowl.

Regarding heating..I never have, unless I have a regular aquarium going. Just keep out of drafts, away from cold windows, and no direct sunlight, that will warm water too much. They are supposed to be best at 80 degrees F, I know mine get a bit colder in winter, they just seem to slow down a bit and don't eat as much and seem ok. Mine have lived up to 2 1/2 years.

One thing overlooked about keeping fish, tropical or otherwise is that we have them in artificial environments. We have to provide for them in ways that nature already does. We have to feed them, maintain pH, temperature, and deal with their wasteproducts. They may come from Oxygen poor environments and developed an adaptation for it, but unless we deal with their water from a biochemical perspective, their ammonia is going o kill them. They could really use an established filter.

I agree, but if a filter is out of the question (even tho some are pretty cheap), then a complete water change daily is in order. Get you buddy a gallon container, nothing smaller. You can keep a milk jug filled for the daily changes. That way the temp will be exactly the same

Water changes are helpful but I'm still concerned about unseen wasteproducts.

I think if you have a larger bowl, the "unseen"---you mean fish pee? A one gallon or more should be dilute enough to dilute ammonia on one small fish..Mine is just under a gallon and I have to admit I do a few partial water changes between the once a week cleaning. O.K. I'll admit it what I really have to do is add more water(& change some too) because my cats like to drink from the bowl. It's hard to descibe but they manage to drink if water high enough but they can't get there paws into it because of height of bowl. Its really heavy and rests inside of another very heavy bowl. I'll probably get in trouble from all of ya'all now for allowing such behavior