Indeed, as also mentioned above, you can use bump (BW) and normal maps together, but personally, I would simply bake everything into a normal map. You need to have colour, roughness and normal maps anyways, right? In most cases, only this much. Why take resources and time for another BW map, if you can add it to your normal, I would say.
I don’t mean to wander far from the topic, just some food for thought: If you want to add to the “normals effect”, you can grab whatever texture you have for the bump, and mix it with your colour, creating a fake AO kinda effect. This Erindale vid, from 19:00 
