Bump mapping procedural mesh.

So, over the past few months as a pet project I have been playing with procedural meshes.
I have successfully got a procedural mesh working how I would like, and using a texture map I am now able to texture individual areas of the mesh how I choose.

I was thinking of now moving into trying to apply a form of bump mapping to the mesh.
I was ‘hoping’ it would be as easy as selecting bumped diffuse, using my texture map, and creating a corresponding normal map to go along with it.

I know now this is not the case as I am just using RecalculateNormals(), so how do I interpolate or ‘get’ the normal values from a pixel location of my image for each fragment? Does the Mesh.uv2 array have something to do with this? I am under the assumption I will not need to write my own shader because the bumped diffuse shader should already handle this should it not?

Thank you for any information and insight!