Haha good on ya for keeping your betta in a tank and not in a "betta bowl"! The bubbles will dissipate. Cycling is really simple, you just need an ammonia source, a filter, and water test kits. You have the filter and the ammonia source is your fish! Just do two 50% water changes weekly for the first 4-5 weeks until your ammonia and nitrite is at 0. Then do a big 70% Water Change at the end. Keep reading up on the subject though, this is just my simple dimple way to do it for beginners. Never do a 100% WC after the tank is cycled, you'll mess up the bacteria. Good Luck!