That's not really true, 'der Bau' can refer to a building, although this isn't used as often as 'Gebäude' and stands more often in the context of 'Altbau' and 'Neubau' (old and new building). The homes of certain animals are called that (e.g. burrow, den or hole - in the German translation of Harry Potter the Weasleys live in the 'Fuchsbau' = fox's den/burrow) and colloquially it's even used for prison.
So, long story short, 'construction' is not the only correct translation.
@ sunaj and Nos I agree with sunja as you see. Your thoughts are OK, but you state yourself that the word "Bau" has the meaning of Haus/Gebaeude in it.
For sure because is actually means it, but is not used as such in the German language. And now you come with all you compound substantives:
They have all their meaning in the language and are used as you pointed out above.
Der Bau as such is used: as constructions site. (construction in progress)
Das Bauwerk, der Fuchsbau, der Altbau/Neubau, and all the others stand for something which is already finished in which other state it doesn't matter. Can be old, new, for animals, and you correctly pointed out: "in den Bau gehen" is (coll.) and means to go to prison/jail.
As "Aufbau" is one of the German words which has more than a handful of meanings in English please refer to: http://www.dict.cc/?s=aufbau
it is not easy but I give it a try.
1st "Der Aufbau" as a term is used to describe the process of the erection of a building/structure or the build-up if you want to call it like this,
but also to describe the way the structure/building was designed.
2nd "Der Aufbau der Huette besteht aus einem Lattengeruest.", The construction/architecture/composition/structure of the hut is based on a timber framework, hence it is an architectual term to describe how the structure is designed, main components, metal or timer frame, brickwork, widespan, self-supporting etc.
3rd If something is built on top of something else, lets say a tower-like structure on top of a solid building, the tower would be the "Aufbau" build-up on top of the base structure.
I use dict.cc quite regularly, along with the other usual suspects, but I still couldn't quite pin this "Aufbau/Bau" thing down. My unabridged print dictionary made me even more curious, as one entry was "construction, building", and the other "building, construction" amongst other things. Still, you've explained that quite nicely, thanks, and I get to add "das Gerüst" to my vocabulary learning system, courtesy of your second example!