Hello!! I’ve used mercerized cotton for kitchen handtowels (for drying hands next to the sink) and it worked great. after a washing it became very soft, and has been absorbent and durable.
the mercerized cotton I used was of a lighter/finer weight than normal kitchen cotton (like sugar and cream) so I had to adjust the pattern a little to keep the desired size.
A cotton-bamboo blend sounds lovely and it would have the added benefit of being anti-microbial! (so they say)
Acrylic on its own might not be absorbent enough, but it scrubs well. a blend might do what you want just fine. I know others on the forum (Jan in CA?) have made dishtowels out of Lion Microspun (acrylic) and said they have worked pretty well.