Yes, for most songbirds the depth should be shallower. If you make a flat shallow end that is 1 to 2 inches deep at most that would be good for bathing birds.
I have a pond in my backyard that is about 24" deep in the center, but has multiple rocks around the periphery that are at the surface, or just below. They love bathing on them, so it is easy to achieve an attractive bathing situation for them.
Good call putting some stones and rock around it - you will want it to look as natural as possible for photography purposes. Those planter dish bottoms work well. You could also just put some flat rocks in the liner, sort of what Randy describes (river rocks, the flat squared one, not the smooth rounded ones, work really well and are easily "stackable").
Last edited by Daniel Cadieux; 04-01-2016 at 11:41 AM.