Why is it bumpier below where the clouds form and once you get above the bases the air tends to be smoothers?
In some sense the question is backwards. But, that really leads to the answer. Clouds form when there is air movement. For example of how clouds can form: when there is local heating, such as due to the sun heating a large black parking lot, the air over that will rise. Flying through that air is not as smooth as in other places. As that air rises up it expands and cools leading to an increase in the relative humidity. If it does that enough it reaches 100% RH and a cloud forms. But, that also leads to a decrease in the energy available to move that air up, so it doesn't keep rising up. So, the air above clouds tend to not have as much energy and movement as below.
So, clouds form where there is air movement, and they "mark" that movement.