So let me make sure I understand the basic idea of what you're trying to accomplish here..
You want to generate a texture that incorporates the lighting in the original texture with the shadowing and highlighting effects that the bump map would provide, thereby baking said shadows and highlights into the original texture, itself, in addition to the flat lighting? Am I close?
I'm not familiar with many modeling packages (only one, to be exact), but I know that XSI has a "bake albedo" function included with Ultimapper, which will allow you to essentially bake whatever the surface of the model looks like into a single texture, bump maps and all. I wouldn't be surprised if other modeling packages include such a feature... the process you'll likely have to follow is this:
1 - Apply the original texture to a square polygon
2 - Apply the bump map
3 - Add a light to the scene to cause the bump map to do something.
4 - Find whatever function your program can provide that will sandwich everything together for you
If you can't seem to find anything, you can use a quick and dirty method that I use to "bake" texture effects without any actual specialized program to help:
1 - Get a square polygon and apply your texture to it
2 - Apply any other texture effects like normal maps or ambient occlusion or whatever
3 - Create an orthographic camera whose aspect ratio is 1:1 and position it so the square polygon fills its entire screen space exactly
4 - Configure your renderer so that there is sufficient antialiasing and enable any necessary rendering effects to get the texture effects to work correctly.
5 - Render. Wait. Wank, perhaps.
6 - The result will be a render of the polygon with everything working together: essentially, you'll have a texture with everything sandwiched down into a single item.
... Assuming I answered the question you actually needed to have answered, the above method can be used in any modeling app that offers the ability to render. I hope this was helpful!