Funny, I've used Bridge since v. 1 and I've never used that approach. I just tried it and you are correct, it doesn't work. Then I opened Bridge 2018 and it didn't work there as well. What was ammusing was that the option of "cut" was in the contextual menu and that didn't work either!
When I want to move a file from one folder to another I just have a Bridge window for both folders open and drag the file(s) from one "Content" Panel to the other.