Not all Blues rhythm guitar parts use chords, many songs sound great with single note riffs instead, often doubling or complementing the bass line. To create good riffs, it is necessary to know several scales and arpeggios. Probably the most common scale in Blues is the minor pentatonic As the name suggests, this scale contains five different notes. Its degrees compared to a major scale are 1, b3, 4, 5, and b7. Here is a common fingering for the minor pentatonic scale in the key of A.
Try running up and down the scale a few times until you have the sound and the fingering memorised. Here are two examples showing the scale ascending and descending.
Most single note riffs which follow the 12 bar Blues progression begin on degrees 1, 4 and 5 of whichever scale they are using. The term "riff" means a short repeating phrase. The more familiar you are with these scale degrees, the easier it will be to learn new riffs. This exercise should help you become familiar with the positioning of degrees 1, 4 and 5 within the minor pentatonic scale.
In many riffs, the fingering for the 5th degree of the scale is on the name strings as the 4th degree, but moved up two frets. This ends up more practical than changing to a different set of strings. The fingering is demonstrated in bars nine and twelve of this exercise. The picking here should be alternating down and up strokes.