There were two pubs that went by the name of the Bridgeman Arms in the Bridgeman Street-Crook Street area. This about the first such pub which lasted from at least 1824 until the 1840s and was situated on Crook Street.
The pub was founded by Richard Makin who first appears as the landlord in the 1824 Bolton Directory. The previous Directory, for 1821/2, had no reference to the pub.
By 1830 the Bridgeman Arms was owned by Jeremiah Hardcastle who died in October of that year. A newspaper report says that he retired to bed one night only to be found dead in his bed at two o’clock the following morning. He died of an apoplectic fit and the verdict given at his inquest was: “Death by the visitation of God”.  By 1836 the pub was run by George Hutchinson.
Interestingly, the address of the Bridgeman Arms was given as Bradford Square which was the name given to the area around what is now Trinity Street prior to the construction of the Bolton to Manchester railway line. The railway opened in 1838.
Gordon Readyhough gives the pub’s date of closure as being around 1840 . Certainly it was a landmark on census reports of 1841.  By then it was being run by George’s wife Peggy Hutchinson and there is no indication as to what had happened to George. Its address according to the census was Bridgeman Street though it is listed as the first property after the junction with Crook Street. In those days Bridgeman Street continued across the railway line to link up with what is now known as Lower Bridgeman Street. In that case it may well have been at the junction of Crook Street and Bridgeman Street but backing in on to Bradford Square. That would put it in vicinity of the Albion Hotel on Bridgeman Street.
Peggy Hutchinson was still running the pub according to the 1843 Directory but it seems to have closed shortly afterwards. However, it isn't beyond the realms of possibility that it changed its name to the Albion.
The Bridgeman Arms name was subsequently used by a beerhouse that opened in the mid-1840s and was situated at 81 Bridgeman Street.
 Manchester Courier, 2 November 1830.
 Bolton Pubs 1800 – 2000, by Gordon Readyhough. Published by Neil Richardson (2000). Lancashire Online Parish Clerk project. Accessed 1 January 2016.
An 1824 Map of Bolton. Bradford Square can be seen in the lower half of the picture.