The Official AKC Bulldog Breed Standard includes this requirement for color:
The color of coat should be uniform, pure of its kind and brilliant. Colors are red, white, fawn, fallow, or any combination of the foregoing. Patterns and markings may include brindle, piebald, ticking, black masks, black tipping, and a minimal amount of black in piebalds. All other colors or markings are a disqualification. 
The merle pattern is a disqualification.
To learn more about the Standard, and our commitment to healthy breeding, please visit The Bulldog Standard.