Watch the Maybellish online guitar lesson by Muriel Anderson from Essentials: Chet Atkins Style
One of the most approachable of Chet's tunes is "Maybelle", written for Mother Maybelle Carter. We'll take some of the techniques and structure and create an easy tune called "Maybellish" that starts with a simple bass-chord accompaniment. Getting the feel of the thumb going back and feeling the groove is the most important part of this style, and also it's the way that Chet claimed to have started playing the guitar. Anchor the side of the hand right next to the bridge to get a muffled sound in the bass. One advantage to this muffled bass technique is that when the guitar is amplified, the bass notes don't feedback as much. It became a signature sound for Chet as it did for Merle Travis and other fingerpickers.
Chet always used a thumb pick - the pick gets a brighter sound on the bass strings especially when muffled. It's up to you whether you'd like to use a thumb pick or just the side of the thumb. Myself, I have used both techniques, requiring a slightly different hand position for each.