Hello. I would definitely look more into the baptism in Rotherham in 1779 under the name Alice Bailey with parents Benjamin and Sarah and this is why. I had been trying for a number of years to find the baptism of my ancestor John Beeley. I eventually found him but baptized under the name John Bailey. His family lived in Masbrough in Rotherham. His father was Marmaduke (or Duke) Bailey. I ordered Marmadukes will and it confirmed that he was the father of my John and the rest of his siblings also baptized under the name Bailey. I then managed to trace Marmadukes baptism which was in Dewsbury and surprise surprise he was baptized Marmaduke Beeley. Marmadukes parents marry under the name Beeley. Obviously i cannot confirm that the Alice Bailey form Rotherham is the correct one, i would advise you to try and look into it a little more. The two names seemed to get mixed up quite often around that area (probably due to accent and being illiterate).
Thanks for the information on the Alice from Rotherham. From the information you have on Bailey/Beeley she is worth a look to see if any family names are common as I cannot find any real proof of where she came from.
Hello again. I have done a little more digging for you. I noticed on the marriage record for Alice at Sheffield Cathedral 1802 that one of the witness's was William Fearnley. I looked for the marriage of William Feanley and he married Sarah Beeley at Sheffield Cathedral 25th Dec 1795. He would have been the brother in law to Alice. Sarah died in Sheffield in 1848. Her age is stated as 77 (although this can always be a year or two out). I searched for a baptism for Sarah Beeley but cannot find one around the time of Sarah's birth around Sheffield. I did find a baptism for Sarah Bailey in Rotherham in 1773 and the father was once again Benjamin Bailey (same as Alice Bailey form Rotherham). I know this does not prove that this is the correct lineage but it is worth looking into.
You have found an interesting connection. It could be my Alice but there was also a marriage in 1804 at Rotherham of a Alice Bailey (Spinster) to William Taylor so a lot more digging will be required to prove the relationships. Thanks for going to so much trouble - you have given me some new ideas.