Watch the Playing A-D-E Progression online guitar lesson by TrueFire from Beginner Guitar Explorations
Lesson Source: Richard Gilewitz's Jump Start Fingerstyle Guitar
Notice how I use economy of motion to minimize the movements I need to make to play this progression.
For each chord, I pluck a different set of bass notes with my thumb. For:
A – I pluck 5th/4th with my thumb.
D – 4th/5th
E – 6th/4th (and then 5th/4th if you want).