If you have a filter, you don't need an air pump
An air pump is used to aerate a betta aquarium. It is not used as a means of decoration (in fact, it can stress your fish out, as we explain below).
Aeration isn’t critical for a betta aquarium.
In fact, if you have a filter, you won’t need it. If you don’t have a filter, it’s better to have an air pump than to not have one, but it’s not critical. And in most instances, betta fish do need a filter.
Bettas have a brilliant system for breathing underwater. They’re known as labyrinth fish, meaning they can take oxygen through their gills or from the surface of the water.
This doesn’t mean they can choose; they need to frequently use both methods to maintain healthy, active respiratory organs.
How does an air pump / bubbler work?
A filter simply aerates the water by stirring it around when water exits the output. This allows gasses to move from the air to the water, and vice versa. A bubbler / air pump works in exactly the same way. It's a common misconception that the bubbles produced by air pumps oxygenate the water, but air pumps are actually designed to cause surface movement — which bettas tend to dislike. Too much movement on the water’s surface can make them feel uncomfortable and stress them out.
So any alternative to an air pump is a good idea. An open lid aquarium allows for a larger water surface area, meaning fresh oxygen will easily dissolve into the water. However, as we know betta fish can leap from the water and an open top aquarium design isn’t the best choice for a betta fish. However, a lid that allows in a substantial amount of oxygen but can stop a betta from escaping (for example, a mesh lid), will work efficiently.
Bettas aren’t fussy when it comes to oxygen, but if you’re keeping your betta in an aquarium with a tight-fitted lid and no filter, an aerator would maintain an adequate oxygen level in the water.
Here's an example air pump on Amazon that we recommend if you do need one.