Cut a length of thread measuring an arm span long.

Thread through your ring base and attach a stopper bead on the inside of the ring near an edge.
This shouldn't affect how the ring fits the wearer. 
Attach this stopper bead securely before you start sewing.

Start at one end with your lighter seed beads and sew two rows of these with the seed beads on the outside of the ring. 

Sew another two rows of darker bronze seed beads. 
Continue to sew rough rows of seed beads in alternating colours until you reach the other end. 

Knot the cord on the underside and attach another stopper bead if you think it will secure your beads better.