21st Century Fabric used to be my favorite fabric covering. It shrinks so well that it does tend to pull from the edges. If you leave plenty of overlap, you'll be fine.
If you are concerned about adhesion, an application of Balsarite will alleviate your fears.
These days, I've switched to Solartex. It is easier to apply, but the colored varieties should be clear coated to make the covering easier to clean.