http://www.rootschat.com/links/01gho/Noting that children's mother was transcribed as Bithia on all the FHS transcripts. ( Sadly) Her name might also have been Elizabeth & her family nickname Bethia.
England and Wales Non-Conformist Record Indexes has
a Bethiah Brown was buried March 1st 1787 Chesham, Buckinghamshire
Bathia Brown death Dec 24 1818 Wooburn, Buckinghamshire ( Is this our Bethia (nee Porter? )
Bithiah Brown buried 30 December 1818 Wooburn, Buckinghamshire
mother: Sarah Brown
Buckinghamshire Parish Registers Chesam marriages
https://archive.org/stream/buckinghamshirep08phil/buckinghamshirep08phil_djvu.txtThere may be more in the earlier marriages ( 1600s) would have to look closer
Two older marriage are:
p. 52 Zachariah Hawks & Martha Porter... April 21st 1701
p. 74 Joseph Porter & Rebecca Dancer ... Feb 22 1735
Within 30 years of each other, these marriages, including the two we know of
p. 119 Jas. Bardwell Browne, of Berkhampstead, Bethia Porter, lic. ... July 4th 1797
*also Jas. Reynolds & Sarah Puddephat on page
p. 123 Robt. Blunt, w., p. St. George, Southwark, Anne Porter, lic. June 17 th 1802
p. 127 Saml. Porter & Sarah Ball, lic. May 29th 1806
*Henry Benning & Eliza Renolds on page
p.129 Wm. Street & Mary Ann Porter, lic. Aug. 16 th 1808
p. 136 Robt. Wray, esq., p. St. Andrew, Holborn, & Eliza Porter, lic. March 31st 1817
*Now see that here are Reynolds galore and several Blunts in there as well...