Watch the Chet Atkins Muffled Bass online guitar lesson by Muriel Anderson from 50 Right-Hand Techniques You Must Know

By bracing the palm of the hand near the bridge, you can experiment with how close to the bridge you place your hand to see how much of the bass you want to mute.

A thumb pick helps to bring the bass back out, and also changes the position of the hand a little since the pick comes out of the side of the thumb. Chet always used a thumb pick, so you might try that for the most authentic sound.