My new thinking is that I need to attach an HBridge to the Shift register
Yes good idea.
How would I make the output pins in the shift register show the Hbridge output
A H-bridge has two inputs, current flows when they are at different logic levels, so you could just connect them like you tried before.
However if you wanted to save on shift register pins you could invert the output of each shift register bit with a 74LS04 (6 bits inverted in one IC), and feed the signal and it's inverse into the H-bridge. In order to save current you could have one of the shift register bits connected to a master enable line for all the H-bridges.