I've got experience of bamboo towelling in washable nappies (not homemade). It definitely holds more liquid than ordinary towelling but it takes a long time to dry and if you are sandwiching between fleece you won't really be able to get it totally dry by tumble drying.
You could perhaps, instead of sewing the bamboo inside fleece, make a sandwich using press studs (or even Velcro?) so you could then line dry the fleece layer and tumble dry the bamboo layer.
Here's another alternative absorbent layer used often in the US for nappies
Also micro fibre (think I've got that right - Thirsties nappies use it!) is often used as an absorbent layer in nappies.