Here's a picture of the bike I'm covering with fabric scraps so far.
As you can see, I have woven fabric strips through the wheels - on both sides - and am beginning to wrap the various tubes with more strips. I tied the ends of the strips onto the spokes of the wheels, but with the tubing, I'm using Elmer's glue to hold it in place. I worry that the fabric on the wheels will sag in our humid weather, but my son suggested some clear coat spray. It stiffens the fabric a bit which should be good. Anyway, it's a work in progress, but a whole lot of fun!