If you look at the GloucestershireBDM

Child's Surname: BITHELL

Child's Forename: Charles

Mother's surname: LONGWARNE

Year: 1843

Office: Gloucester Newent

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CLDS have a birth of an Edward BITHELL - 9 June 1822, Bodenham, Hereford, parents John & Ann

Can see Edward BETHELL/BOTHELL on the 1851 and 1861 census, and looking at the 1851 census, Herefordshire born Bodenham - his children are aged 3 and 1 - Edward BETHELL married 1845, Leominster District.