Talk about raising an old thread from the dead!
Anyways, I think walking or a mountain bike will be the only viable way to travel if things really went south. Travelling any kind of road in a vehicle is just an ambush waiting to happen. If you want to be safe you'll have to stay off the roads. I've also reconsidered the whole idea of bugging out. If things really got bad where are you going to go that isn't in equal or worse shape?
I've been into riding for years, but recently decided to incorporate it into my SHTF strategy. No need for gas. Can go places a car can't. Better than walking!
Might look for a good deal on a cart or one of the baby carrier things to go with it.
The bike baby carriers can be found cheap once the kids outgrow them and hold stuff better than babies.