It is essential to use correct right hand technique when fingerpicking single note runs. Generally there are three or four positions for the right hand. The right hand first position is used when a lick is based around the first three strings. Allocate the right hand thumb (p) to the 3rd string, the right hand index finger (i) to the 2nd string and the right middle finger (m) to the 1st string.
The following example is played within the first position. Special attention should be given to the suggested right hand fingering.