Here is an easy beginner blues boogie that you can play on one string. You need to use two fingers to play this. Use your first finger on the 2nd fret and your 3rd finger on the 4th fret and create a rocking motion in between the finger changes. This boogie is in 4/4 and the notes you play will be quavers or 8th notes, so play them slightly quicker.
The chord patterns to accompany this are as follows:
A A A A
D D A A
E D A E
Strum each chord to last for 4 beats. By the end of the pattern you will have completed your first 12 bar blues!
The boogie should sound like this: