Here is a sample with different backgrounds. Personally, they take away from the wheels. The black allows the wheels and diamonds to float on the quilt and draws your eye to those components, which is what you want in this case. Of course, it is all up to you.
I love the bicycles. It would be the perfect back to this quilt.
Yes you can piece this easily. I will help you. Not paper pieced, just straight piecing. One step at a time...