Put on the paper mask and your eyewear. You want to keep from inhaling any paint fragments and you definitely don't want any of them getting into your eyes.
Apply a coat of thinner to any existing paint on the bulkhead with your paint brush. After letting the thinner soak for several minutes, rub the paint off with your wire brush.
Follow up the wire scrub with a Brillo pad, all over the bulkhead. This will score the surface somewhat, making it more likely to adhere to the new primer.
Apply a layer of primer. After you let it dry, add another coat or two as needed to give a consistent color.
Put the first coat of paint over the primer with the brush or sprayer. Allow it to dry and then apply a second layer (and more, as needed) to give uniform color.