Liberty print, or any light weight quilting fabric, works really well for this project. Both of these bangles were made with 90cm strips of fabric that were about 3cm wide, with one edge folded over about half a centimetre and pressed.
Starting on the inside, wrap firmly around the bangle on a slight angle, overlapping and fabric as you go (making sure the un-pressed edge is covered). Just before you get to the last wrap, fold the unpressed edge over with your fingers (so there will be no exposed frayed edges), wrap it around the bangle and then trim so it can be glued down on the inside of the bangle. Fold over the end of the fabric before gluing (I just used craft glue) to give it a nice finish, and either hold it until the glue bonds, or clamp it with a clip or peg. Warning :: these are addictive! Wooden bangles to cover are available in the Yardage Design online store.
Have a great Thursday!