After watching a couple videos on Youtube, it is pretty clear that I might want to provide some tips. These are just simple things to help you get the most out of the game and are not any way cheating.
First: During Story and Versus you do not have to wait around for more balloons. Pushing up on the controller will make more balloons load into your playfield. A row of 6 at a time. Don't wait, get more balloons as soon as you need them.
Second: Your playfield collapsing has to do with how many balloons your opponent has popped. On Normal your field collapses every 40 balloons popped by your opponent.
Third: Save those balloons. The more balloons you pop at one time of the same color will cause your opponent to get hit with gray balloons. They start getting gray balloons with 5 or more balloons. But the payout isn't 1:1. It gets exponentially bigger. The more you pop, the more they get buried by. I'm not sure what the ratio is, but if you pop 5 balloons they only get 1, however if you pop 10 balloons, they get more than 5.
Finally: Keep your eyes on what your opponent is doing as well as your own board. You need to be prepared if they are close to popping (or just did pop) a massive amount of balloons of the same color. The last thing you want to do is have your board all loaded up with a single color so you can setup a big payout of gray balloons on them just to have yourself buried by gray balloons which end your round.
This is just a few tips and general info to make the game more fun for you.