Betty is probably a daughter of John and Alice Walmsley.
31 May 1841, Betty Unsworth, Widow, daughter of John Walmsley, a weaver married John Snelson son of Thomas (both sawyers) at St Peter's, Bolton. In 1843, another Elizabeth, daughter of John Walmsley from Middle Hulton, also a sawyer, married Thomas Gillibrand. This other woman was a spinster and Elizabeth, not Betty.
In June 1841 there are no Snelson families on the census. There was John and Betty Nelson (35 & 30) with William (3) and John (4 mo), living at the Farmers Arms, Lever. This is another family Betty Nelson, nee Welsby).
In 1844 Betty and John has a son Thomas Snelson. The MMN was UNSWORTH (but should be WALMSLEY). In 1850, Robert was born with MMN correctly recorded as Walmsley.
In 1851, John and Betty (both 34) were at Lupton Street, W Bolton with Eliza Snelson (11) and Thomas Snelson (6).