The technique I think you are looking for to achieve this is known as Parallax Occlusion Mapping and is an extension of Parallax Mapping.
Parralax Occlusion Mapping is a technique to interpret which texel to pick based on the viewing angle relative to the surface normal while taking into account the surface displacement provided by the bump map. Keep in mind that when you know which texel to pick you also know which (u,v) point on the triangle surface is being viewed.
What you should interpret using this technique is the texture coordinate for the given triangle that is illuminated by a given light source projecting a ray in a specific direction. So from here you should be able to calculate the per-pixel lighting incident on a fixed surface for the purpose of light baking similar to how you would without the bump-map (whatever technique you are using for this).
This should suffice for baking your diffuse illumination for that surface into some data source (added on top of the standard colour texture maybe?). However, handling specular illumination may prove more of a challenge and possibly can only be done in real-time as it is dependant on the viewing angle/position as well as light and geometry information.
This technique is often used in real-time and isn't so expensive that it necessitates baking. Consider adding it as a real-time extension to your system first as you will probably need this long term for dynamic objects to fit well with the rest of the scene.