The BB who married Mary Ann Nightingale, is more likely to be the BB who was born 1 Nov and baptised 3 Nov 1798 at Great Yarmouth, the son of Thomas Barrett and Mary Woolard that Eddie has identified above.
There is another BB baptised at Great Yarmouth on 22 Sep 1797 the son of William Barrett and Martha Mountford, but it looks like he died young and was buried at Great Yarmouth on 13 Mar 1799. This is from searching FreeREG, so these are transcriptions, but usually reasonably reliable.