Using an air pump isn't recommended for betta fish. Not only do they dislike the agitation associated with water surface movement, but it can also cause stress. A simple filter in the tank should be more than sufficient to meet bettas' air needs.
In fact, bettas are capable of breathing oxygen from the surface of the water, using a special organ. They have also been known to survive in oxygen-depleted environments. However, this doesn't mean that you should not add an oxygen pump to your tank.
The purpose of an air pump is to add oxygen to your tank's water, similar to a filter. However, an air pump isn't the same as a filter, as it doesn't pass water through a sponge or other filter media. Instead, it moves fresh, oxygenated water to the top of the tank. This increases the rate of gas exchange at the surface, which means that your bettas will be breathing healthier water.
Using a bubbler is another way to improve the oxygenation of your tank's water. A bubbler is an attachment for an air pump that creates bubbles that float up to the surface. Bubbles are a good way to increase the rate of gas exchange, and to remove toxins from the water. The bubbles are not an actual oxygen source, but the agitation that they create is enough to increase the rate of gas exchange.
Another way to improve the oxygenation of your water is to use live plants. These plants can help produce oxygen when they take in carbon dioxide. They are also very cheap to purchase, and will help keep your bettas healthy. However, they should be paired with a good air pump to ensure that the water is properly oxygenated.
Another thing to consider when considering an air pump is the size of the tank. If your aquarium is small, an air pump may be unnecessary. However, larger tanks are more difficult to maintain an oxygenated water level. Larger tanks have less surface area than smaller tanks, and it can be difficult to oxygenate water in such environments.
If you do decide to get an air pump, you'll want to get one that's gentle on your bettas. A gentle air pump will reduce stress, and will be better for your bettas' wellbeing. The more stress your bettas endure, the less likely they are to survive.
Lastly, the best way to improve the oxygenation of your tank's waters is to make regular water changes. This is especially important if you have a lot of waste in your tank. This is because stagnant water will accumulate harmful bacteria and parasites, and can even lead to poor water quality. Water changes can range from 25 percent twice a week to small ones daily.
It's not surprising that betta fish prefer to breathe atmospheric air rather than swimming around in oxygenated water. A bubbler can help improve the oxygenation of your tank's surfaces, but it isn't necessary.