John William Bowler first came to Port Jackson on HMS Rattlesnake in August 1836. He was on board HMS Rattlesnake in the process of conveying Governor Bourke to Port Phillip when they came upon the stricken immigrant ship Lady McNaughten. John Bowler was placed on board when it was found that the surgeon J.A. Hawkins was also gravely ill. Sir Richard Bourke later gave an account to Lord Glenelg......
Sir Richard Bourke to Lord Glenelg.
My Lord, Government House, 10 April, 1837.
I embrace the earliest opportunity afforded since my return from Port Phillip to give your Lordship some account of the Emigrants by the ' Lady Macnaghton ' whose distressing case will probably have become known in England before this letter can be received. The Lady Macnaghton was met and spoke by H.M.S. Rattlesnake (in which I was proceeding to P. Phillip) about 200 miles to the Southward of Port Jackson. On receiving an account of the alarming fever which prevailed on board and under which the Surgeon Mr. Hawkins, since dead, was then lying incapable of duty, assistant Surgeon Bowler, R.N., was immediately sent from the Rattlesnake to supply his place, and I wrote at the same time to the Colonial Secretary at Sydney, intimating to him that it would probably be necessary to place the Lady Macnaghton in Quarantine on her arrival in Port Jackson. Mr. Bowler found the vessel in a most deplorable state, as will appear from the letter addressed by him to the Colonial Secretary on arriving at Port Jackson. Ten adults and forty four children died on the passage; and, since arrival, four adults (including the Surgeon Hawkins) and nine children have sunk under the disease. Assistant Surgeon Bowler has been seriously ill in consequence of the exposure and exertions attending his employment, but I am happy to say that he is now out of danger. 
John W. Bowler returned to Australia in March 1839 with immigrants on the Aliquis.
In 1841 he was stationed at Jamaica and employed as surgeon on the vessel Victor. On 4th March he was court-martialled for drunkenness and sentenced to be severely reprimanded and placed at the bottom of the list. 
John William Bowler was employed as Surgeon Superintendent on the John Calvin to Van Diemen's Land in 1848 and the Hashemy to Western Australia in 1850....
From Dr. Bowler, R.N., Surgeon-Superintendent of the Hashemy convict ship :—
Sir 20th May, 1851. I have much pleasure in reporting my arrival in England, and of informing you that the convicts sent out in the ship 'Hashemy under my superintendence, from Portland to Western Australia in July last, were landed at Fremantle, in October following, in a healthy condition. I have great satisfaction in stating that (with a slight exception) they conducted themselves throughout the voyage in the most orderly and becoming manner, giving me very little trouble, which I duly reported to his Excellency the Governor, with a strong recommendation for a mitigation in their punishments, as awarded to the prisoners of the 'Scindian,' should they continue to behave well; and up to the time of my leaving the port—a month after disembarkation— the Comptroller-General, Capt. Henderson, R.E., spoke of them in the same favourable terms. 'I was much assisted in my duties by the warders, and found them of more essential use than the guard of pensioners.' There appears to be a great demand for convict-labour at the Swan River Settlement. Report on the Discipline and Management of the Convict Prisons. 1850
John William Bowler was appointed to the Phoebe Dunbar to Western Australia in 1853.
The Hampshire Telegraph reported his death in 1864 -
We have to record the death of Wednesday of Dr. John William Bowler, surgeon-superintendent of Portsmouth convict Prison. The deceased officer entered the navy in 1837 as assistant-surgeon. His last appointments were to the Victor, 16, Capt. Dawson, on the West India station; the Hazard, 18, Capt. Bell, in which ship he took part in the operations on the coast of China, and for which he received the China medal. His last service afloat was in the Alarm, 26, on the North America and West India station from which he returned in the summer of 1847. Dr. Bowler was a retired Deputy Inspector of Her Majesty's Naval Hospitals and Fleets. 
The Late Dr. Bowler.
The officers of the Portsea Convict Prison, of which the above lamented gentleman was for several years the Surgeon-Superintendent, anxious to testify their high respect for his many excellences of character, raised a fund among their body for the purpose of erecting a suitable memorial to him. This has taken the form of a handsome mediaeval marble cross, which has, within the last few days, been placed in Haslar Cemetery, where the remains of Dr. Bowler are interred. The cross is 3 ft. 6 in. high, and stands on a bold base or plinth, also of marble, 12 in. high, this being placed on two solid Portland stone steps, making a total height of 6 ft. 1 in. The shaft and arms of the cross are chamfered and stopped, and the lathe united to stem and head by a circle of marble widely splayed and serrated on the edges, producing what may be termed a rayed nimbus, which gives great richness to the design. The arms and head of the cross terminate in plain foliations. On the broad splays of the marble base or plinth inscriptions are cut in characteristic letters, the capitals being rubricated. On the east side is the inscription:
- In memoriam. John William Bowler, Surgeon, R.N., obit November 16, 1864, age 61 years. On the west side is the following : - This Cross is erected by the officers who served with him in the Portsea Convict Establishment, as a tribute of esteem and affection. On the north side are the words, 'Thy will be done; 'and on the south, ' God be merciful to me.' The memorial forms the entire width of the west end of the grave, except a few inches on each side, and the north, south, and east sides are enclosed by a massive Portland double chamfered curb, on which is placed an appropriate iron rail, supported on ornamental standards.