You will get some, just watch out. There are some mail order shops that sell. Check the woodworking magazines for their adds.
I recently figured out, that simple beech boards from my homedepot are quite nice to cut.
Also do they now have beech plywood in stock - fantastic quality, much better than the baltic birch!
If you're searching for special wood (not just bb ply) you can search for "music wood" that's used for building musical instruments. it's mostly around 1/4" to 1/8" thin. Check for B sorting - much cheaper.