In order to get this achievement, as well as a Rank A - You must first collect each part of the Bike.
(taken from the Dead Rising Wikipedia: http://deadrising.wikia.com/wiki/Motorbike
The bike is missing 5 essential parts in order for it to run:
Gasoline Canister, found by the gas pumps
Wheel, able for purchase at the Still Creek Pawnshop for 5000 $.
Bike Forks, found locked in a shed
Handle Bars, used by Jason Wong as a weapon
Engine, found in an alley between Ed's Friendly Barber Shop and Still Creek Movie Theater.
Once you have completed this (and defeated Jed after giving Katey the shot at 7pm) you then have the chance to jump on the bike and escape the Army.
You must return to the Bike itself in the Garage and a cutscene will take place. Once this has ended, you will be in charge of the Bike itself. You must then use this to drive out of the valley of Still Creek. The camera angle is bad, but you should be able to get it in one shot like I did. Once you have escaped, and the final cutscene starts your achievement should pop. And you've just got your A Rank :)