How big is the bed?

The "shortened" version (ie where we were able to dig a little) is about 22ft long and about 8ft wide. It runs along the back of the yard- behind it is scrub/wooded area, so I only need to worry about edging the front and sides. It's in sort of a rounded rectangle, right now. Eventually I hope to build a rock wall along the back of it.
Thanks-

That's a pretty big area. Many people would argue with me, but I like to use old railroad ties. They are relatively cheap, sturdy, and long-lasting. You can find them much cheaper at rail salvage places than at stores like Lowes or HD. They are 8 feet long, so it would take you only three across the front and one on each end. Obviously, this is mostly useful for raised beds rather than ground-level ones!

I'm sure many other people will have alternate solutions!

Given the shallow depth-to-rock you are facing, I would strongly consider raised beds. Do you compost? If not, start a compost heap and start scavenging composting material from neighbors etc--that'd be the cheapest way to go, though it will take some time. Use compost to fill the beds. You probably don't need them that deep--depending on what you are growing. Maybe 6 to 10 inches? Also, have you heard of Lasagna Gardening? Check it out if not...it might be something you like.

You might look around for fill dirt for sale in your area--sometimes people moving earth will sell the fill dirt cheaper by the truckload than by the bag at the graden store. Just be sure you don't get any more of that orange-red clay!! ;)

Growing up, my folks used RR ties as fenceposts and for use in landscaping/raised beds. I probably wouldn't use them for a veggie garden, or any treated lumber, but for flowers you would be okay--amazondoc hit the nail on the head about the rail salvage places (don't know of any here though). They may be a cheaper & faster route than rock. IMO, I like rock better for looks & toxicity issues. And depending on where you are, you may have other resources to draw upon (downed timber, construction materials, etc).
Patience will definitely be your biggest asset...The soil texture will change with your persistence and over time in planting. Too bad we can't change where top-of-rock is in parts of Middle TN without heavy equip or dynamite :)

There are other materials to build with besides rr ties. Box The picture and the link (box) are a couple of examples that I'm very happy with. With all of your rock, that is an even better material to build a raised bed with. Rock takes a lot of experimenting with as you put one in to see how it sits & then try another. Compost and/or manure mixed in with the existing soil is the most desireable thing for building a garden with.