Primer is not needed between old paint and new paint, but you need to scuff the old paint before applying the new. Primer is required for any bare metal. You should use a wax and grease remover before and after scuffing.

I've been experimenting with Dupli Color acrylic enamel color and clearcoat. It becomes fairly durable after it dries for at least a month. I may try painting a bike with it, even though I have very good spray equipment. At least I won't have to clean the gun.