The B748 is described in the 1922 Road Lists as Ayr (Link to Pier). It runs along the left bank of the River Ayr and so is a counterpart to the B746 which ran on the right bank but was declassified early on.
Maps claim that the B748 starts on the A719 (former A77) immediately to the south of New Bridge and heads west along South Harbour Street. However, this road is eastbound only and is, in practice, part of the A719 one-way system. The B748 only appears for real at a mini-roundabout one block west.
The road continues west along the river bank. After passing a corner of the citadel wall the road enters a 20 zone and runs through a district of modern housing. Eventually the road bends to the left away from the river. The B748 ends here and the road ahead is unclassified.