Assuming you're aiming for bamboo about 10-12 ft high, a 12"x12" planter seems a bit small - it might be OK, but I'd give it some more width if you can, maybe 18" wide or more. You don't give details about the wood front, but if you make it out of 3 or 4 stacked 4x4's, you need to make it *very* strong to resist the eventual pressure of the bamboo rhizomes. You can attach the 4x4's to each other with big lag screws, but the biggest problem is attaching the botom 4x4 to the concrete slab. Caulk isn't nearly strong enough. Construction adhesive might be strong enough, but it would be better to drill holes into the conrete under where the 4x4's will be, and epoxy big bolts into the holes to attach the bottom 4x4's to. Drainage is important too. You could make 1/2" - 1" holes every foot or so near the bottom of the bottom 4x4's, but you'll probably get some staining of the adjacent concrete from the soil runoff.
You might also check on the "Container Gardening" forum here.