What makes snap-on roll-up reflective bands want to roll up?
If you were a kid in the 90s, you probably remember slap bracelets. They're basically the same thing. Usually made up of something like a bit of old tape measure (though you can make bistable structures out of many things). 

You can make a slap bracelet by taking a bit of tape measure (say 6 inches) and rolling it up (gently but tightly), with the number side up (i.e. on the outside of the curl). See this video for an example of how to make it. 

For what you want to do (and for riders in general), I recommend getting velcro reflective bands.