Nope, no problem washing cotton and bamboo and any other fabric all together. I've done it for a long time with no problems. The only thing to watch for, and this would apply to all fabrics, is to not wash brand new, never washed diapers, with used ones. The oils from the brand new diapers could potentially transfer to the used ones and cause them to repel.
This would be especially so with hemp (and maybe bamboo, I'm not sure) as it's heavy in oils. Honestly though, regular cotton, bamboo or hemp diapers probably wouldn't be affected very much. The absorbancy might be slightly reduced for a while but they probably wouldn't repel. Pocket diapers or any diaper lined with fleece, suedecloth or any kind of 'stay-dry' fabric are much more prone to this. They're more prone to repelling in the first place so it wouldn't necessarily take much to put them 'over the edge' so to speak.
I've had that exact experience washing new hemp diapers with a load of dirty ones, including some pockets. My pockets started repelling like mad after that and I couldn't figure out why. It wasn't till I thought back to my new hemp diapers that I figured it out. Stripped the pockets and they were fine after that.