I thought I'd try this out and post some demo renders anyway. It was a useful exercise for me, and I'm wary about giving out advice without proving for myself that it works as I expected!

This first render shows a marble sphere with largish specular highlights from two white lights. You can see the specular colour is white and the specular value is 1.0. (The sphere is actually reflective too, but it makes no difference to this exercise. Those highlights are not coming from the Reflect node, but from the Specular node.) Ignore the small spheres, they are from something else I was doing in the laboratory.

The next picture will show what happens when I use a greyscale image, such as a bump map, to mask these specular highlights.

"If I were a shadow, I know I wouldn't like to be half of what I should be."
Mr Otsuka, the old black tomcat in Kafka on the Shore (Haruki Murakami)