I have family connections to the Bartlett Family that emigrated to New Zealand in 1842.Here is the information that I have, I hope it proves relevant to you!
John(37) and Maria (34) Bartlett emigrated from Engalnd from the port at Gravesend with their children,Joseph (12), Thomas (10) Ann (7), Mary (3) and Robert (infant),on board the Olympus on 16 June 1842.They landed in the port of Nelson in New Zealand on the 28 October 1842.
My connections are through Joseph and Thomas who both married my Great-great grandmother Anne White who was also on board the Olympus with her family. Anne had a daughter (Annie Eliza) before her marriage to Joseph.Joseph died in 1863 (drowned) and she married Thomas in 1866.Thomas and Ann had 5 children, I only have the name of their 3rd - Alice Francis Bartlett. Thomas died in 1907.
Annie Eliza married Edwin Barker and had 9 children. Upon her death (1895) her half sister Alice Francis bought up her children and eventually married Edwin in 1924.They had no children.Edwin in my Great Grandfather.
The Bartletts are buried in a private cemetry in Fabians Valley in Blenheim.I have a picture of the Bartletts family house in Fabians Valley if you would like me to send you a copy - its not an original and is of limited quality however!
Hope this is of help to you.Would be interested to hear more about your Bartlett connections!