Basically, if your stick movement is bouncy you should see it in the Advanced settings for each axis. A stable stick should keep the numbers static, a bouncy stick will more or less scroll the digits.
There's two possible reasons for stick bounciness: either the pots are spiking or the springs are so weak that any vibration (like a bypassing car or kids jumping in the yard) makes the stick move.
In any case start with a proper calibration to see if that helps. You can do it first in Windows and then in the game, the latter is more important but the former can help. If it's the pots, they can be cleaned (vigorous stirring may help in mild cases) or replaced but that requires some knowledge. In both cases you can add some Dead Band i.e. some slack before the movement gets registered. You can also add some Damping which smoothens sudden movements. When applying those use baby steps to keep the stick as sensitive as possible.
