Once those bubbles make it to the surface, they dissipate fairly quickly. They will hang around, though, if they can "attach" to stuff on the surface (plants, aquarium walls, etc.). It's not something to overly freak out about, BUT sometimes the gases that get trapped in water can be none too nice for your fine scaly friends (nitrogen, ozone, etc.).
When you do water changes, try to release the gases before you add new water to the aquarium by agitating the water. If you have a pressure hose (like the little one with the flexible hose on some kitchen sinks), using it to spray the outside of a bucket full of water will cause a lot of those bubbles to escape right away. Stirring the water semi-vigorously with a wisk can also be effective, but make sure to bang all of the sides of the bucket with it, and I recommend trying to find a plastic wisk. You never know what the metal ones will leave in your water. Finally, adding new water to the aquarium VERY SLOWLY should prevent the containment of anything that's left, and the rest of the gases should be released into the air somewhere between the bucket and your aquarium.
Again, this isn't something to be overly concerned about. Toxic gas ingestion from "tiny bubbles" MIGHT kill one fish in 500...certainly not one of the ten most wanted suspects in fishy deaths. But I've found that it doesn't take too much effort to avoid it. When I see little bubbles in a betta's aquarium, I expect it to mean he's building a nest!