if you want to mix two normal maps, take a look at this question, which explains very well how to do it: How to Combine two Normal Maps?.
However, to create a more visible bump effect, try to use the Bump node, and plug the bump map into the Height socket, as here:
I think this setup gives you more control via Strength and Distance values. You can also plug your normal map into the Normal socket, it's up to you. Just remember to set Non-color for bump and normal maps.