I also have a Harriet Hodgkinson Bobart b 1817 at Woodstock. Her father was Gamaliel Hodgkinson Bobart and her mother was Elizabeth Churchill. Could this be your ggg-grandmother? Gamaliel was the brother of Tilleman Hodgkinson Bobart b 1770, the coachman in the portrait.

The name Tilleman Bobart or Tilleman Hodgkinson Bobart was very common in the family. Tilleman the coachman's obituary says:

//Obituary, January 1839: At Oxford, suddenly, in his 67th year, Tilleman Hodgkinson Bobart, esq. Superior Bedel of the Faculty of Law, and formerly Commoner of University College, of which Society he became a member, May 5th 1790. Mr Bobart was much beloved by his private friends, and highly respected by all who knew him. He obtained his appointment of Esquire Bedel in 1815. He has left a widow and a numerous family.//

He married Mary Smith in 1795. They had 7 daughters and 2 sons: Tilleman Hodgkinson Bobart b 1801 (d 1867 Derbyshire) and Henry Hodgkinson Bobart b 1806 (d 1854 Parramatta, NSW) who is my ancestor.

Your Tilleman married Harriet Elizabeth Stratford in 1824, the same year their daughter Harriet was born. He would be the one you mention in the 1841 census as he would have been exactly 40.

The name Tilleman goes back to Tilleman Bobart b 1660, who was the great-grandfather of Tilleman Hodgkinson Bobart. The first Tilleman had no sons, so when his daughter Elizabeth married Henry Hodgkinson in 1716 they kept her name and their children used the surname Hodgkinson Bobart and their descendants continued using both even into the late 1880s. My family dropped Hodgkinson after the death of Rev Henry in 1854.

I have a fair bit of information about the Bobart family if you're interested.