how to work it out in Gimp? Here is a very easy node setup in blender:


when I apply it to a plane it results into:


suppose if we want to bring the result for a bump map, we could take it in gimp with the subtract mode set on the wave texture we get a result such as this:


the results are quite different because of the 'fac' value in the node in blender:



how can we do fix this in gimp so that I can get an image file to use it in blender as a bump map?
If turning the layer opacity down doesn't fix it, make sure you have only the top layer (in Gimp) set to subtract. The bottom should be normal.

However, I don't think that's your problem. I think you are just using the musgrave and wave from Gimp, which has a different seed value (and maybe a different algorithm). Plug the texture directly into an emission shader set to strength of 1, and render that. Then do so for the other texture. Be sure to save both rendered images!
Now load them into Gimp as layers.

I hope this helps. Because I don't have the files, I can't think of anything else.