One note of caution: I've put in at least 10 new bulkheads and driven maybe 20,000+ miles with them. No problems until a recent trip I hit a real pothole with my crappy axles (new axles next month) and the body flexed just enough to pop one bulkhead (it was basically right over the axles) out of the aluminum extrusion. When everything came together again, they didn't quite match up and the extrusion ate the top of the bulkhead--turned it into feathers and sawdust for about the top 2" (lots more damage than the total motion would indicate, due to the splitting nature of plywood) and along about 18" of radius.
This was on my 27' Overlander. It doesn't show any other, ok, much other, evidence of hard ride--no rear separation, etc. But it obviously flexes enough to cause at least an inch deformation of the trailer cross section up along the ceiling radius, I'm thinking more like 1.5" or 2", worst case. I don't think putting bulkheads only at a rib will help. Just be cognizant that at the maximum flex point of the trailer (over the axles) you need to think about what kind of lateral restraints you use at the top of the bulkhead, eg, from about 4' above the floor to the top leading edge of the bulkhead. From what I can tell, there is no real problem along the vertical part of the bulkhead, from floor to about 4' up.
When I replace that bulkhead I'm thinking it doesn't really need lateral support up high. If I do anything, I'll make a deeper wood channel device to ensure that it doesn't slip out again.
On another note, I haven't seen any damage or marks that would lead me to believe that compression is a problem, eg, trailer ceiling coming down and squeezing the bulkhead down. Maybe I'm lucky and have enough flex in the bulkhead (1/2" plywood with a 3/4" edge trim of solid maple) to allow for some compression.
By the way, if you make shop-built cabinets (nice and square and rigid) and install several along one side as I have done, be careful not to tie them together too strongly--you will be making a long beam and as the trailer flexes you may wind up tearing the cabinets apart laterally because they can't flex to match.
Lynn, with a 22', you're probably not in the flex danger zone, but I'd still think about what flex could do to your installation.