More with the Thumb.

You can use the thumb to pick out a melody on the base strings. If the notes you want to play do not fit the roll just stop the lick, let your thumb do the walking and jump back in when it feels right. This will actually make your playing more interesting.
I am using the C chord in the first position.

Start at the third fret on string 6 then second string frets 0,2,3.	6,5,5,5	T,T,T,T
Now start the lick making the last note of this run the first note of the lick.	6,5,5,5- lick	T,T,T,T-lick
You can run down this sequence and change to G.	5,5,5,6-lick	T,T,T,T-lick