There's an Isabella Bicknell aged 47 living in Clifton, Bristol (just a couple of miles from the marriage location) in the 1841 census. Highly likely to be James's mother, his father having died.
"England and Wales Census, 1841," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:M7MZ-3F3 : 13 December 2017), Isabella Bicknell in household of Willm Harman, Clifton, Gloucestershire, England; from "1841 England, Scotland and Wales census," database and images, findmypast (http://www.findmypast.com : n.d.); citing PRO HO 107, The National Archives, Kew, Surrey
Ignore the age "correction" - it's 47 on the image. That would correspond to a birth in 1793/4 which fits well with James being born c. 1813.