I've only used bamboo once and it was a bamboo/cotton blend batting. I didn't notice that it stuck any better, but I've always thought my cotton batting grabbed pretty well (I use mostly Quilter's Dream). I will say it was softer than plain cotton, but now in the quilt I don't notice any difference.
Plain 100% cotton seems to be what I like the best. I live in the south, gotta support my farmers, ya know? :D