mrcurtis, the bouncing of the wood is called "chatter". It happens when you are either using a reverse tooth blade or the blade is in upside down. Don't be discouraged by reverse tooth blades. They eliminate tearout and give you a nice edge on the bottom of your piece. It reduces the need to sand. I use them most of the time. It takes some practice to move your wood and hold it down at the same time. Depending on the size of your piece, your finger tips or the side of your pinkie will do the job. Practice, practice, practice. It will come in a very short amount of time.
As far as the quality of your saw, I have seen amazing things come off the most basic of saws. It makes moving up to a better one that much sweeter when you can accomplish great things with the old one. You will see a great improvement in your cutting when you get your FD blades. It's not the cheap saw that is the culprit in most cases, it is cheap blades.
At any rate, with each project you will see an improvement and things get easier. Enjoy and happy scrolling.