Hey no problem! I am glad I can help others with the information this site has teached me :)
The undergravel filter is really just for aeration, and you wont be able to cycle with that. You need a place for the beneficial bacteria(BB) to grow like on a sponge on a sponge filter:
If you run a airpump or powerhead with the undergravel filter you can buy a sponge filter for a couple of bucks online, replace the undergravel with the spongefilter and start cycling. It takes 1-2 months and requires a decent testing kit like the API master kit(costs 17bucks on amazon) but it will free up alot of time doing water changes and it will help you keep your betta healthy and happy. So it takes some work in the start, but then when its done cycling the BB is working for you and you get less work each week ^_^
I would buy a water treatment that locks ammonia either way, I use Prime from seachem. It detoxifies the ammonia in the water for 24-48 hours and makes the uncycled tank alot safer for the fish. You can't use it in stead of waterchanges and you will still need to do a wc every two days, but it will keep his water safe in between changes. A small tank gets toxic really fast unfortunatly!
If you get to exchange the heater for a smaller one I would do that or maybe you can pay a few dollars extra and they wil let you exchange it for a Adjustable one? they are really the safest for both you and your fish :)
I know this is alot of information to gulp down, and I know its really annoying having to buy new things all the time, but by upgrading to decent stuff once
you save alot of grief and money in the long run :)
Edit: forgot to give you the stickie on cycling: Cycling