Bulteel was commissioned lieutenant on 22 July 1778 and appears to have been employed in home waters during 1779 aboard the Hydra 24, Captain Thomas Lloyd, before later going out to Jamaica. Here the commander-in-chief and his apparent patron, Rear-Admiral Joshua Rowley, promoted him commander of the American-built brig Bloodhound on 24 September 1782, which vessel he retained until the end of the year, his commission being confirmed by the Admiralty on 4 July 1783.
In April 1786 he commissioned the sloop Termagant 18 for preventative service in home waters and in the North Sea, and on 6 February 1787 he resorted to arms to capture a large and prolific smuggler, inflicting casualties of ten men killed and fifteen fatally wounded before taking the vessel into Hull. At the end of the year, having sailed from Plymouth on 21 December, the Termagant was driven out of the Channel by such a strong south-easterly storm that she fetched up in Lisbon, having been given up for lost and with her pumps working around the clock to keep her afloat. She arrived back at Falmouth at the beginning of February 1788 and Bulteel left her shortly afterwards.
He was one of many officers posted captain on 22 November 1790, being appointed for purposes of rank only to the Amphitrite 24.
In January 1795 Bulteel commissioned the recently re-captured Castor 32, taking her out from Portsmouth to the Mediterranean in May under the orders of Rear-Admiral Robert Man, and paying her off in September 1796 upon returning home with a convoy from Corsica under the orders of Vice-Admiral Robert Linzee.
After another period of unemployment he was appointed to the Belliqueux 64 in May 1799, and he served in the invasion of the Netherlands during August to October. In December his vessel was at Chatham, and in May 1800 she arrived at Portsmouth from the Downs before departing on the 15th with the East India convoy. On 4 August off Brazil the convoy fell in with three French frigates which promptly scattered on the assumption that the Belliqueux and the six East Indiamen were sail of the line. Displaying commendable panache, Bulteel and the merchant vessels undertook a chase, resulting in the uncontested capture of the Concord 40 by the Belliqueux, and of the Med e 36 by two East Indiamen. The Franchise 36 escaped, her captain having failed to prevail upon his commodore that the Indiamen were not in fact men-of-war. In early December the Belliqueux arrived back in the Downs with the China Fleet and the Adamant 50, Captain William Hotham, whereupon Bulteel relinquished the command.
He was advanced to flag rank on 25 October 1809, vice-admiral on 4 June 1814, and died at Plymstock, Devon on 27 August 1820.