These are the details you should use to order the birth certificate:
Beatrice SEWARD, Mar qtr 1904 Bristol 6a 207.
Be aware that if, as expected, she was born as the illegitimate daughter of Lilian Seward, there will be no mention of adoption, or of Ernest & Kate Sandford, on the birth certificate and it is highly unlikely that her joining their family will have been formally documented elsewhere (other than perhaps in workhouse records, which may or may not survive). As I mentioned in an earlier reply, formal adoption was brought in much later on.