CHORDING AROUND A SINGLE NOTE REQUIRES AN UNDERSTANDING OF WHAT CHORDS YOU CAN USE AT ANY GIVEN TIME. LET'S TRY THIS DRILL:
IN THE KEY OF C KEEP YOUR PINKY ON G:
CEG
BbEbG
ACDG
BDEG
AbBDG
GBDF#G
NOW ADD THE BASS:
CG / CEG
GbE / BbEbG
DA / ACDG
CG / BDEG
AE / GBDF#G
BA / ABDG
ONE CLUE IS: WHAT CHORDS HAS THE G NOTE IN IT? AND WORK FROM THERE