Grace's Guide is the leading source of historical information on industry and manufacturing in Britain. This web publication contains 132,164 pages of information and 209,699 images on early companies, their products and the people who designed and built them.
Bourne, Bartley and Co of Mayor Street, Manchester were machinists between 1838 and 1840.
Possibly built a locomotive 
1839 Bourne, Bartley and Co advertised 'A locomotive for sale with six of their patent wheels, now undergoing a most satisfactory trial on the Liverpool and Manchester Railway' 
1840 January. Partnership dissolved. '...the Partnership lately subsisting between us the undersigned, John Frederick Bourne, John Bartley the elder, and John Bartley the younger, carrying on business in Manchester, in the county of Lancaster, as Engineers, Millwrights, and Manufacturers of Patent Wrought Iron Wheels, under the firm of Bourne, Bartley, and Company, was this day dissolved by mutual consent...'
1841 Pigot & Slater's Directory of Manchester & Salford, 1841 does not link Bourne and Bailey as a company, but gives the following information: John Frederick Bourne, engineer, house 25 New York Street; John Bartley, engineer, house 37 Richmond Street
1841 May Their patent of 1838 for wheels offered for sale.
The Liverpool Daily Courier, 2 Sept 1882 describes the discovery of a manuscript book full of information relating to the Liverpool and Manchester Railway. The relevant paragraph reads as follows.
"The volume includes copies of a considerable number of official reports, bearing the initials 'E.W.' (Presumably Edward Wood - Ed) One of the earliest of these is addressed to Messrs. Bourne, Bartley, and Co. of Manchester, who seem to have inquired about the character of the work performed by an engine of theirs, the St. George. 'E.W.' made experiments in April, 1839, and details the results, which are hardly worth while repeating here, though the Manchester firm were doubtless rejoiced to learn that 'the engine has performed her work quite satisfactorily.'"
No. 31 was the first engine completed in the year 1839. It had a four-wheeled loading bogie, with unequal wheels, one pair being 3ft. 8in. diameter, and the other 2ft 10in., the "single” driving wheels being 5ft. diameter. This engine was built to the order of Messrs. Bourne, Bartley, and Company, and was intended to be sent to America, but ultimately Messrs. Bourne sold it to an English firm of railway contractors.