Familysearch gives her father as John Bridson in the marriage record.

1881 census for 7 Cambridge Ter, Douglas [RG11/5605 f.49 p.7 sch37]
Robert Webb head mar. 27 Shopman, born Glossop Derbyshire
Sussanah wife mar. 24, born Castletown
Ellen S daur 19 mo. Douglas
James Bridson brother-in-law 16 Sailor, Castletown

WEBB, Ellen Sephton 21 Aug 1879 Douglas 227 d/o WEBB, Robert & BRIDSON, Susannah Jane
WEBB, Susan Hannah 14 Aug 1881 Douglas 325 d/o WEBB, Robert & BRIDSON, Susannah
WEBB, Samuel 8 Sep 1883 Douglas 433 s/o WEBB, Robert & BRIDSON, Sussanah Jane
WEBB, Robert 17 Oct 1884 Douglas 489 s/o WEBB, Robert & BRIDSON, Susannah Jane

1891 census 7 Cambridge Ter, Douglas [RG12/4689 f.59 p.6 sch.35]
Robert Webb, h, m, 37, Shopman (Fancy Dealer), Glossop, England
Susan, wife, m, 33, Castletown, Isle of Man
Ellen, d, 11, scholar, Douglas
Susan, d, 9, scholar, Douglas
Samuel, s, 7, scholar, Douglas
James Bridson, brother-in-law, s, 26, Castletown

1891 20+18 Strand St, Douglas: there is a Samuel Webb aged 60 a Jeweller & Fancy goods dealer from Warrington, wife Charlotte, 43, born Cheshire, and son Henry 24 born Douglas.

1901 census 7 Cambridge Ter, Douglas [RG13/5304 f.45 p.6 sch.32]
Susannah J Webb, h, wid, 43, Living on own means, Castletown
Ellen S, d, s, 21, Shop assistant (Fancy), Douglas
Susan H, d, s, 19, Douglas
Samuel, s, 17, Clerk, Post Office, Douglas

Susannah Jane Bridson born 1857/58 in Castletown with a brother James born about 1865 and father John Bridson:

1871 census for Derbyhaven Rd, Castletown [RG10/5777 f.220 p.30 sch.169]
John Bridson, h, m, 48, Boot & Shoe maker, Castletown
Susan, w, m, 33, (Boot & Shoe maker’s) wife, Castletown
John K, s, un, 18, App shoemaker, Castletown
Susan J, d, un, 14, scholar, Castletown
Thomas C, s, un, 12, scholar, Castletown
William R, s, un, 10, scholar, Castletown
James M? H?, s, 6, scholar, Castletown
Margaret H, d, 3, Castletown
Walter E, s, 1, Castletown

Familysearch: James Norris Killey Bridson c.2 Ar 1865 Castletown, s/o John Bridson & Susan

Maiden name for John Bridson’s wife Susan not given in the children’s baptism records.

Looking at wife Susan’s age in 1871 and age of eldest child, I suspect she is a second wife.

Familysearch: John Kneale Bridson c. 11 Apr 1852 Castletown s/o John Bridson and Jane

Could this be Jane?
Lawson Burials: Jane Bridson, 30, Malew, buried 28 May 1852.

1851 census Bowling Green, Castletown [HO107/2526 f.46 p.4 sch.74]
John Bridson, h, mar, 28, Shoemaker, Castletown
Jane, w, m, 29, Braddan
Margaret Killey, mother of wife, U [?], 66, Malew

So, if this is the right family, at least you have Susannah J Webb as the daughter of John Bridson, shoemaker of Castletown, and his second wife Susan. Presumably the 1841 census and church registers should help get further back.