Why does it take two days to reach the ISS? Orbital mechanics?
That's a good guess. They want to conserve fuel and have the closing speed as slow as possible. Less chance of a bad accident that way.
The best way to figure that out is to calculate a mission yourself. Where is the ISS, where is the launch site, what are the main constraints on launch, what are the operating parameters of the shuttle boost phases. If they were going to simply hit a target like the Chinese satellite killer the trajectory would be very oblique; if they are going to rendezvous at half a foot per second they need a tangential orbit.