Is it the Hawkeye 201 air pump? That's the air pump that comes with many small tanks, it puts out about 1/4th the amount of bubbles as other small air pumps I've seen.
Also for betas in the past, we used this:
Use a T and a Valve to create a cheap and small "Gang Valve" and relive the excess pressure out the valve, and connect the other 2 ends of the t to the pump and the tank. Normal gang valves do not work because they cant hang onto the back of many one gallon tanks, the small tanks don't have a lip in the back. I add the air stone on the end of this to muffle the sound of the air pump from the air bleed from the valve.
I think that a tiny tiny amount of bubbles and filter action could be good for a Betta.