Quote:n my mind, bump's range should be [ -128, 127 ] to render as wanted.
Unfortunately, I don't see how to do that. Perhaps, it's not the right method.
Perhaps not. Is this some method you use in some other graphics application ?
The bump map can be a layer or another open image. Grayscale or desaturated, blurred gives a rounded effect. The docs https://docs.gimp.org/2.10/en/gimp-filter-bump-map.html
For a bump layer, either under the image or visibility turned off.
There is a drop down menu for layer modes in the bump-map dialogue. Filters -> Map -> BumpMap
A demo of that as an animation. https://i.imgur.com/02CEk47.mp4
Otherwise, give an example of an 'expected' result.