The first mention of a BOWDEN in NSW newspapers was a Matt BOWDEN, first assistant surgeon, who arrived in 1803 as part of the Civil and Military Establishment of the
intended Settlement.
http://nla.gov.au/nla.news-article625895
Ros
adding : http://adb.anu.edu.au/biography/bowden-matthew-1808
(doesn't mention family 
and I guess he was too young to have a 10 year old daughter)
He did have children, a daughter named Anne, and a son named Matthew, and a son named William Henry BOWDEN see below.
There are a number of lasses in NSW in 1801 who may have been Mary BOWDEN and the surname may have been recorded as BOWEN, ROWAN, ROWEN, RAGAN, etc ... many variations.
The C of E burial register for St Phillips, Sydney (NSW) has an adult named Mary Bowden buried 12 July 1802. This is clearly NOT the Mary Bowden who arrived under a transportation sentence per the Earl Cornwallis in June 1801 as that Mary is listed in later Musters, eg 1806, 1811, and later and in the 1820s is shown as the wife of George TILLY in the Windsor district of NSW.
The NSW Colonial Secretary’s papers has interesting entries in their index, including noting Matthew BOWDEN’s will of 6 Oct 1811. Ancestry has partnership arrangement with NSW State Records,
http://colsec.records.nsw.gov.au/default.htm 6 October 1811. Anne Elizabeth BOWDEN is a beneficiary under her father’s will. He was Mathew BOWDEN.
6 October 1811, Matthew BOWDEN Junior is a beneficiary under his father’s will.
6 October 1811, William Henry BOWDEN, a beneficiary under his father's will.
I have not searched for Mrs BOWDEN, mother of these three to check her given name
Matthew BOWDEN, Surgeon, ……. 6 Oct 1811 his will……. Died suddenly October 1814.
The Col Sec's index has just ONE Mary BOWDEN arriving in 1801.
JM
