Hi Cody,
I became interested in the South African War many, many years ago and have collected a fairly large library of reference material. The Canadian Mounted Rifles (CMR) was the name that was used for several different Canadian units as follows:
a. Second Contingent - 1st and 2nd Battalions, CMR. The 1st Battalion was formed around a regular cadre from the Royal Canadian Dragoons (RCD) and was redesignated as the RCD while in theatre. The 2nd Battalion was based on the North West Mounted Police and after the 1st Bn adopted the RCD title, dropped the 2nd Battalion. These units were each two squadrons strong and were equipped with Mk1 Lee-Enfields and Colt revolvers. It is my opinion, based on my study of the war, that the RCD was the best Canadian unit on a man-for-man basis that served in South Africa, and probably ranks amongst the best overall.
b. Third Contingent - 2nd Regiment Canadian Mounted Rifles. This unit was raised and paid for by the British in Canada in 1902. As recruiting was good, it ended up six squadrons strong. The regiment was equipped on British scales so pistols were restricted to officers and a few other appoinments. This unit was considerable service in early 1902, including at Harts River.
c. Fourth Contingent - 3rd, 4th, 5th and 6th Regiments, Canadian Mounted Rifles. These units, each of three squadrons, were quickly raised by the British in 1902 as the ease with which the 2nd Regiment was recruited showed that there was ample manpower willing and able to serve. Unfortunately they arrived after the end of the war and except for a number of members who joined the South African Constabulary, were returned to Canada and discharged with indecent haste.
As revolvers were supplied for the RCD and CMR, it is possible that your Mauser may have belonged to a member, probably an officer, in one of the later units, probably the 2nd Regiment CMR as Bloemfontein is well inland. Officers were supposed to provide their own pistols and this may be the case here.
As an aside, I believe there was a South African unit called the Cape Mounted Rifles, so . . .
Do you have a model number, place and date of manufacture and serial number for the pistol? I have a few references re small arms used by both sides and may be able to help. As I am not an expert on small arms, I caution you not to expect the moon, but you may get lucky.