Soil is right. You don't need to bury the fence unless you're trying to thwart something like voles or other underground burrowers that attack the plants from below. You can bend the wire, as Soil described, or you can just lay boards along the bottom of the fencing. That's what I did, to keep my little dog from getting out of my yard by digging out under the fence.
I used 16' 2x12 boards, but 2x10, or even 2x8, would work just as well, I'm sure. And they certainly don't have to be new boards. Get old ones, if they're available to you for free.
You could even rip a sheet of plywood into strips, if that's what you have around. If all you have is 4x boards, strap a couple lengths together with cleats or even something like strips of plumber's tape screwed down. Wouldn't necessarily be pretty, but it'll keep the critters out.
Lay the boards flat on the ground, butted up against the outside of the bottom edge of your fence.
"Isn't it enough to see that a garden is beautiful without having to believe that there are fairies at the bottom of it too?" - Douglas Adams