Betta bowls are among the worst things pet stores do to the aquarium hobby... it's on par with telling customers they can keep a BP in a tank with Aspen, no humidity, and saying no thermostat is needed.
Bettas absolutely require at least 2.5 gallons of water, a heater (or temps at 75-80 if that is your room temp), and 300% need a filter. The filter exists to give a place for beneficial bacteria strains to live and perform the nitrogen cycle (which is the process fish waste is removed by) and to remove physical debris in the water (poop, dust, free floating algae, etc.) As well as to circulate the water and promote oxygen exchange so the fish is more easily able to breath.
Care info for betta fish can he seen here, since I'd end up just re-typing it out.
https://bettafish.org/care/
The film you're seeing is buildup of bacteria and/or algae in the stagnant water and is not healthy for the fish. This is the same stuff we change reptile water bowls regularly to remove. (If you wouldn't want a reptile or mammal to drink it, you definitely do not want a fish to live in it.)
The only way to "get away with" using a bowl is by doing daily or every 2 days 100%, complete water changes. This means tanking the fish out, dumping the entire bowl, filling with new water & dechlorinating it. And even still a betta bowl is truly too small of an environment. Think of it as equivalent to keeping a 3 or 4 foot adult male BP in a 10 gallon tank.
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