One thing is that you may 'deminish' the value of the bed by refinishing it. Only an Antique Appraiser (or a good book) would know.
BUT, if you want to proceed, wipe the paintable areas with mineral spirits and let dry. Then, damp dry later on. Then, use a light coat of SPRAY paint, not canned paint, to PRIME the bed. Then, use a can of SPRAY Finish Paint in the color desired. You may want to do an 'intentional imperfect' paint job because if you want to preserve the details, use a few LIGHT coatings instead of a couple 'heavy' coatings. Heavy coatings will 'run' on you. So, don't try to do the perfect job on the first coating. Let a day go by for the paint to REALLY harden (although the can may say you can wait a couple of hours or so.)