If you make a Bull Rush while charging can you use any remaining movement you had left to move with your target? For instance, if you have a Speed of 30, charge 10 feet, and beat the opponent’s CMB by 15 with a Bull Rush could you push the opponent back 20 feet and follow him?
You can move with the target if you wish but you must have the available movement to do so.
So, yes. You don't have to, but you may.
Agreed. Plus, visually it's awesome to imagine charging someone with your shield set and ploughing into them, lifting them off the ground and running them 15ft back.
It is funny that you mentioned ploughing into somebody with a shield since I'm actually hoping to use this with Shield Slam.