Many people in your situation use what is called Table Top beds. Check out this discussion.
http://squarefoot.creatingforum.com/t41-table-tops-take-sfg-to-a-higher-level

Thanks, some pretty interesting designs there.

I recently read a book called "Stand Up and Garden" by Mary Moss-Sprague which discusses using raised beds at about waist height using a 36" tall frame. Ms. Moss-Sprague fills her frames with straw up to about 8" from the top and then fills up the rest with the soil mix of her choice. She also provides details for setting up a drip irrigation system.

I don't see any reason why you couldn't use that method, or even fill up the bin with shredded leaves, letting the lower layer become leaf-mold over a year while gardening on top of it. You could even put wood and branches in the bottom, a layer of straw, and then soil mix on top to make a hugelkultur bed.

Here is a link that might be useful: Stand Up and Garden

If you have a transfer center near you that gives away free leaf mulch, you can fill the lower 24 inches with leaf mulch. You can also use straw or any type of organic filler. I know one woman that put limbs, straw and leaf mulch on the bottom and her garden soil mix on the top.