Apart from being KC registered with no endorsements on the pedigree, generally your bitch must have successfully passed all the breed-relevant tests for hereditary conditions and judged to be a good example of the breed.
Wonder if OP means At stud to approved bitches only as seen in stud ads? If so all info already given would apply plus stud dog owner would be happy for dog to beused on the bitch
By this I would undersand that the bitches pedigree would be compatible with the dogs. Both could be perfectly lovely examples of the breed but due to a common fault in them or their ancestry the Stud owner would not approve the bitch to come to his/her dog.