I've never quilted with bamboo batting so I couldn't tell you how well it quilts. I've heard that its anti-bacterial and eco-friendly since bamboo is a very renewable source....that's about it.
On the subject of alternative fiber sources, Keepsake Quilting sells one called EcoCraft Eco-Friendly Batting. Its a 50/50 blend of cotton and PLA (made from corn). Personally, I don't know how well it quilts. It says it offers the performance of synthetics and the peace-of-mind of natural fibers. Soft, durable...hand or machine quilted up to 4" intervals. These are what the prices are:
Crib: $8.99
Twin: $19.99
Full: $23.99
Queen: $27.99