Some more tips:

If you're looking around, you'll tend to turn your shoulder when you turn your head. Hand is connected to arm is connected to shoulder so when you turn shoulder, you pull the bar that way. If you look over the left shoulder, you tend to steer a bit left.

To avoid this put your left hand on your thigh, hip, knee, anything but the bar. Then turn around.

You can also look under your arm to see where things are behind you.

You can hold your bars near the stem. It's easier to hold a straight line when it's harder to steer the bars accidentally, and holding the bars near the stem helps immensely.

Relax your grip. You should be holding your bars as if there was an egg under your fingertips. Okay, small egg, but no death grips, not unless you're about to crash or something.

cdr