Bamboo is a very stable floor material, and it's not cheap.
Saving a few dollars in the subfloor could be false economy, and while modern particle boards are very stable as well, I can imagine what your builder would say IF a problem developed with the bamboo, and you decided to install a sub-floor against his recommendation!
Cheap insurance I reckon, although I've never had a problem with a particle board floor WHICH WAS CAREFULLY LAID, and glued.
Cheers,
P