I understand that as you make a semiconctor smaller, to the quantum dot size, you can control the size of its band gap, and this is due to the fact the material is now a smaller size than the electrons ideal Exciton Bohr Radius. So if you add more atoms (and therefore electrons) the particle size increases and the band gap will get larger as it "wants" to be closer to the Exciton Bohr Radius, and if you make the particle smaller the band gap has to get smaller. I think that that bit is right.

My question is that does this mean that in a bulk material the band gap is the same size as the Exciton Bohr Radius, and is the exciton Bohr Radius different for different materials (I guess it must be) and what determine the size of this radius in a bulk material.

I hope that makes sense, thanks