How do I remove a bridge header without getting errors?

Go to Build Settings of your project, find Objective-C Bridging Header row and remove its contents.

Since removing the bridging header or even just leaving it without any content often causes build errors, the quick workaround I've found is leaving the header with nothing but the following two imports:

#ifndef BridgeHeader_h
#define BridgeHeader_h

#import <Foundation/Foundation.h>
#import <UIKit/UIKit.h>

#endif

Go to targets file->Build Settings->Swift Compiler - General, delete the contents in the same line as Objective-C Bridging Header