How collector-base junction in BJT works
The key to it all is the minority carriers in the base.

Your suspicion is correct that if all you had was the CB junction it would just become a diode.  Reverse biasing this diode does not give you any current.  The p-base of an npn is full of holes and the n-collector is has lots of electrons.  In reverse bias the majority carriers move away from the junction on both sides and you do not get any current, just like an normal diode.

The tricky part happens when you forward bias the base-emitter junction.  The holes in the p-base move towards the BE junction and the electrons in the emitter also move towards the junction.  Some of them annihilate each other but because of the doping inequity a lot of the electrons from the emitter pop through into the base!!!  As a result they can keep propagating through the base to the collector and you get the collector-emitter current that you were hoping for.

You should take long look at the diagram labelled Lecture 7 - Slide 12
http://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-012-microelectronic-devices-and-circuits-fall-2009/lecture-notes/MIT6_012F09_lec07.pdf  Holes are green and electrons are blue.