You could contact Lichfield Record Office as they hold the wills for the Royal Peculiar of Bridgnorth (which are not currently online).
https://www.staffordshire.gov.uk/leisure/archives/contact/LichfieldRecordOffice/home.aspxThe British Library and Shropshire Archives - shropshirearchives.org.uk - also hold some other records for the peculiar.
Also there's this useful though paid site:
http://www.bridgnorth-lists.co.uk/Search/SearchWill/index.phpwhich lists two wills - Barrett in 1642 and Barratt in 1828.
As far as burials there's two at Birmingham and one at Worcester that are about the right age for your Samuel:
Samuel Barratt, aged 45, of Coleshill St, buried 09 Jan 1834 at St Philip's Birmingham
also Samuel Barratt, aged 49, of Fleet Street [Birmingham], buried 28 Aug 1836 at St Philip's Birmingham
or Samuel Barnett, aged 53, buried 08 Jun 1842 at St Martin's Worcester