You should be using wheel chocks on both sides of the trailer regardless of whether it is bouncing or not. The chocks are to keep the trailer from moving forward or backward or twisting when you unhook from the tow vehicle. They should always be the first thing on and the last thing off.
Good chocks will also help with slight forward/backward movement but you need to keep in mind that your trailer is sitting on rubber tires and springs so it is going to move a bit no matter what you do other than putting it up on concrete blocks. There have been a couple of good suggestions above to help with the slight movement but don't expect to get rid of all of it.
When we stay for an extended time, like when we are in Florida for the winter, I put
aluminum jack stands under the frame right in front of the wheels near the middle of the trailer. I also use good
Rotochoks between the wheels.
Barney

