Welcome to The Bunting Society11:20PM UTC - Sunday, 18 March 2018 Contact Administrator. Please include your username.
You have posed a problem of adoption which is not helped by having incomplete records on the subject. I tried two approaches.
Firstly looking at the trees we have and which are derived from our "Pedigree" database of Bunting names. As most of our dates have been acquired from the General Register Office (GRO) an April birth will appear in the June Quarter. Searching 31,884 entries for someone born in Jun 1957 produced a list of 21names. Eliminating 10 boys and those who died young, left 11 girls and guess who headed the list - Carol. You had said Elizabeth was your Mother's name and there was only a Mary E from Warrington who didn't seem likely from a proximity point of view.
Secondly I turned to the specific GRO births we recorded several years ago. Again searching for births in Jun 1957. The likely candidate seemed to be the following although it is still quite a way from Stafford.
1957 Jun Elizabeth E Bunting Coventry Reg. Dist. 9c 1067 Mother's surname - Ling.
Does this seem to marry in with the information you have? Please don't go and purchase the certificate until you have sought advice and data, as a direct descendant, from the Registrar's staff about the adoption agency. Realise also that sometimes skeletons from the past are not always welcome.
The Societies records do have a marriage between a Bunting and a Ling but the age of at least one of the participants is doubtful. Let us all know how you get on. Michael.