I agree with Rosie: you need the marriage certificate to see what it says about Charles' father.
There are several Charles Bell births in and around Newcastle upon Tyne c. 1883.
Harriet Bardsley was also at 2 Lancashire St in 1901. In 1901 she reckons she was born c. 1844 (ie 5 years before what she says in 1911) in Miles Platting. She's already a widow in 1901. Florence Pollock, a niece, is also with her, as is a presumably related Joseph H Bardsley, although he's just down as a boarder.
I've not been able to spot Harriet on the 1891 census, though Florrie/Florence Pollock is at Sheridan St, Manchester, living with her parents Alexander & Sarah Pollock. Florrie is a trouser finisher.
I've not looked in any great detail, but the only likely entry on the 1881 census that I could see for Harriet (assuming she was already married by then, which I think would be likely) is with her brother-in-law John Yates, at 55 Lodge Street, Manchester. She's already a widow. John Yates' wife is Mary and his mother-in-law Harriet Gloag is also in the household. That could mean that Harriet's maiden name is Gloag, and indeed there is a marriage of Hannah Gloag & Luke Bardsley on 15th June 1873 at St John's church in Manchester. Luke Bardsley died Q3 1874.