The A845 was the original number for what is now some of the B881 and A844 on Bute.
It originally started in the island capital of Rothesay at the B877/A844/A845 triple point by the pier and headed south across the island to Ambrismore and then around the coast to what was the other end of the A844 at the B881 junction at Kingarth. Later, in the 1920s, when the A844 was extended to form an island ring road the A845 was curtailed at Ambrismore. The route is still shown in the 1988 Readers Digest Atlas, but was later downgraded to be a northern extension of the B881 - see that route for a full description of the road.
The 1922 MOT Road List defines this route as: Rothesay - Meikle Grenach - Kilchattan