I always found the idea of the zombie plague spreading too fast for a reasoned military response to be plausible. I think it's reasonable to assume that you would have at least 48 hours of confusion wherein a large portion of your population is taken down/infected.
Now, I don't know about the rest of the world, but in the US, I can see several days of debate and arguing about what to do, with a lot of people arguing for following of CDC quarantine policies and for the search for a cure first before authorizing military action against sick american citizens. I am sure there would be borders and checkpoints set up, with soldiers being authorized to engage if engaged first, but no offensive actions ordered....then it's too late.
Yeah, in the case of a Zombie outbreak our beuacracy would be our greatest weakness.
If a Zombie outbreak happened the best place to be in my opinion would be small town america. Somewhere in Kansas, plenty of flat land around the house to see what is stumbling your way, farm machinery to "plow down" the zombie hordes and plenty of food/fuel in the form of corn in a grain bin, and water that can be easily pumped via a solar powered cattle well (they do exist) or windmill.