When Felicity plans to use the motorcycle to power the computer, she states that everything with an electronic circuit was fried by the EMP, but being an internal combustion engine, the motorcycle can run and power the computer. However, the motorcycle has an electronic ignition system, so after an EMP, it would not run either. If the motorcycle was from the 1970s, then there would be a chance it still used mechanical ignition points and ignition coil to generate spark. Also, the alternator on the motorcycle would be fried due to the electronic voltage regulator and then diode pack. But even if it wasn't damaged, the power of the motorcycle alternator would be insufficient to power the computer.
Running the motorcycle to power the computer would reduce the available oxygen even more and fill the bunker with carbon monoxide.