Since Sidebottom existed as a surname in Tintwistle there is a possibility Mary married someone local to the village. A search of Sidebottom marriages in St. Michael Mottram-in-Longdendale on the IGI married to Marys gets
JOHN SIDEBOTTOM
MARY WOOD
Marriage: 24 OCT 1830 Mottram In Longdendale, Cheshire
JAMES SIDEBOTTOM
MARY FIRTH
Marriage: 12 JUL 1824 Mottram In Longdendale, Cheshire
SAMUEL SIDEBOTTOM
MARY HOWARD
Marriage: 12 JUN 1821 Mottram In Longdendale, Cheshire
JOSHUA SIDEBOTHAM
MARY WINTERBOTTOM
Marriage: 18 APR 1808 Mottram In Longdendale, Cheshire
If any of these is the correct marriage and it is a bit of a long shot, the earliest marriage would be the likeliest.
Joshua and Mary had these children baptised in Mottram.
SIDEBOTHAM, Charles
Christening Date: 24 Mar 1811
Margaret Sidebottom
Christening: 10 APR 1814
SIDEBOTTOM, James
Christening Date: 10 Dec 1815
Jemima Sidebotom
Christening: 28 JUN 1818
Betty Sidebottom
Christening: 25 FEB 1821
Kitty Sidebottom
Christening: 03 AUG 1823
Christiana Sidebottom
Christening: 01 APR 1827
Joe Sidebottom
Christening: 05 JUL 1829
Mary Sidebottom
Christening: 02 SEP 1832
This appears to be the family in 1841
HO107 110/2 folio 17 page 28
Wagstaff Street Dukinfield Cheshire (like Marple a parish in Stockport)
Mary Sidebottom 55 Cheshire
Ann Sidebottom 33 Cheshire Stretcher?
James Sidebottom 25 Not born Cheshire Corder?
Jemima Sidebottom 20 Not born Cheshire
Betty Sidebottom 20 Not born Cheshire
Betty Sidebottom 18 Not born Cheshire
Joe Sidebottom 12 Cheshire
Mary Sidebottom 9 Cheshire
The unmarried Sidebottom daughters are together in Dukinfield on the 1851 census (it could just mean their mother had died).
1851 census HO107 2237 folio 341
Wagstaff Street Dukinfield Lancashire
Ann Sidebottom 42 Mathern, Cheshire, Head Cotton Piercer?
Betty Sidebottom 30 Stalybridge, Lancashire, Sister Cotton Piercer
Kitty Sidebottom 28 Stalybridge, Lancashire, Sister Cotton Frame ?
Mary Sidebottom 18 Stalybridge, Cheshire, Sister Power Loom Weaver
All very interesting but absolutely no evidence of a Hannah Winterbottom marriage to a William Brierley and also tricky to find both a Mary Winterbottom and a Hannah Winterbottom of roughly the right ages baptised in Mottram with the same parents, where one of them doesn't die young, so this Sidebottom family remain an unproven possibility.
Not sure what look up you are requesting for a search on Ancestry. If you search on Sidebottom you are searching on the woman's maiden name and Sidebottom was Mary's married name.
Regards
Valda