Hi Jane Inskipp,
These two births registered in NSW, in 1888, and 1890.
36944/1888 BYE ALBERT J ROBERT EMILY WENTWORTH
37420/1890 BYE ERNEST M ROBERT EMILY WENTWORTH
If you purchased, either one of those certificates, it should give the age of Robert BYE, and his birthplace. That way, you could rule this family in, or rule them out, as being your Robert BYE.
https://familyhistory.bdm.nsw.gov.au/lifelink/familyhistory/...Mary