I use a quite different technique - a single thick coat of gesso roughly applied. Then the lathe is set to a suitably slow speed (to avoid the white stripe on the smock!) and the gesso is textured with a coarse round brush. The sort you often see for sale cheap.
The green/blue bowl is textured with an affro comb. If you see what hair I have left you would see I have no other use for such a comb! Other impliments can be used for texturing such as toothed adhesive spreaders and things like that.
With the airbrushing, remember to add paint gradually, you can build it up easily enough but once overdone it can be difficult to fix. Because I'm not looking for a smooth surface I finish with satin finish aerosol acrylic lacquer. I'm not looking for a shiny finish.
Don't be afraid to experiment because if you don't like the result, it's easy enough to turn the surface back to bare wood and start again.
I never try to achieve a smooth surface to the gesso but if you did want to do that, you just let it dry and sand it.
I have some other ideas I'm planning with gesso so watch this space.