Yeah. Not to put too fine a point on it, but my woman is not exactly large, and she does not pad the bar before squatting. And she is in her 40's like me.
Anything between yourself and the bar decreases the contact between the bar and your back, which increases the chances of the bar rolling. A thick pad can artificially raise your center of gravity as well.
In addition to the advice you have already been given, pull your shoulder blades together, then grip the bar solidly. Pull your elbows down slightly and pull the bar hard into your traps. Imagine that you are trying to bend the bar across your upper back. This may suck to get used to at first, but having a heavy squat roll down your back because you did not hold the bar tightly sucks even more.