Two nitpicks however. The US Strategic Petroleum Reserve. the largest in the world, has a 160 day supply of oil on hand. I think it was mentioned at some point that they were at day 60 something since the zombie thing started? There should be plenty of petrol around, assuming distribution(a big assumption) continued.
As to headshots being the only way to stop a walker. Unless the CDC doctor was keeping physical changes to walkers a secret, the only change is in the brain stem. That means over-pressure(which is the the main way bombs kill people) will kill walkers as sure as a headshot. Whether the brain is turned to mush by a bullet or over-pressure, the end result is the same. Also, limb wounds and such might not kill a walker instantly, but they still have blood, they still have internal organs that require certain processes to work. Just because walkers are governed by pure instinct doesn't make their biology any different from ours. They'll bleed out just like any other human.
To add to the first nitpick, the Strategic Reserve accomodates ALL U.S. usage (personal consumption AND manufacturing consumption), so if it is all accessible and well rationed out, it might conceivably last even longer than 160 days. Once the powers-that-be saw the extent of the situation, I really don't think more tanker trucks would be heading to the local QuikMart to replenish those tanks. Those resources would be dedicated to military response and civilian evacuation (if any). So our intrepid group might not be able to find gas as gas stations would be emptied out by people trying to get the hell out of Dodge, or burned to the ground by people starting a firefight around the place.
Regarding headshots, if the bullet entered the Z's eye sockets or mouth and blew right through the back of the skull, there might not have been enough energy dumped into the target for hydrostatic shock to pulp the brain stem; in much the same fashion that a 9mm (or even a 5.56 at close velocity that doesn't tumble) will frequently blow through a human target without dropping it immediately, hence the preference for .45 and .40 rounds, which tumble and fragment and deposit more of the round's energy into the target.
Someone else already handled the bleed-out portion.