I have an iOS project written with Objective-C. I created an Swift class in the project, the bridging header file for accessing objective-c in Swift is generated successfull
For me the solution was to create a new target. For an unknown reason, the target that I had didn't have that "Swift Compiler - General" settings and thus no to "Objective-C Generated Interface Header Name" field. Having that field specified in the project was not enough.