The E B E section is the most common chord shape you'll see as you learn. It's the equivalent of a power chord on a guitar. If you want to get fast with one hand get used to keeping your thumb and pinky about an octave away from each other. In this instance that means the low E and high E.

Your instinct as you hit each note might be to use your thumb pointer and middle and move you hand but it will help you down the road if you get used to looking at the individual notes as a chord keep you hand in place as you hit eat note in the chord. In this section I would think about it like A B E is one chord. Then E B E is one chord going up then back down with the same fingers then move you hand into a B E B shape to hit the last 2 notes. Does that make sense?