i have never seen or tried bamboo, so don't have an opinion.
i love Quilters Dream batting. i haven't tried any of their poly or blends, but the 100% cotton is pure joy to work with. i don't do much hand-quilting, but it's been great the few times i've tried. like most, it's pricey but, if you can afford the cost up-front, you can buy it by the case to save money over the long-run. QD offers a poly batting made from recycled plastic bottles. If i was going to chose a batting based on environmental issues, that would be the one for me.
my second choice is Warm & Natural (or White). it's been easy to work with, it's easy to find on sale, and feels like it will hold up well over time.
when cost is the biggest factor, i skip batting altogether. i buy dirt-cheap polyester blankets. less than $5 for a twin size - which can be enough for at least two baby quilts. i wash them first. they're not as easy to work with as cotton batting, but much easier than traditional poly batting.