Hi Sandy I have just found some Bulmers in my family and they lived in Great Ayton. James Bulmer (Christened about 1750) married Jane Coniers on 18 June 1776 at Great Ayton They had the following children:- William christened 28 April 1777 Great Ayton Sarah Ch 17 September 1778 Great Ayton Jackey ch. 4 September 1780 Great Ayton Thomas ch 3 January 1783 Great Ayton Jane ch 4 October 1784 Great Ayton Susannah ch 22 October 1786 Great Ayton James ch 21 November 1789 Great Ayton Jeffrey ch 27 February 1791 Great Ayton Henry ch 4 March 1794 Great Ayton Easther ch 9 October 1795 Great Ayton
Susannah Bulmer married John Dixon on 22 October 4 May 11806 in Great Ayton and they had Thomas Dixon christened 21 February 1810.
There isn't a lot of distance between Stokesley and Great Ayton - so there may be a family link between your Bulmers and mine.