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No, no bayonets. They wouldn't have had a spot to put them, as they had a special uniform type for off-duty, the 'walking-out' uniform. The primary difference with this uniform was the fact that it had a plain white belt -no weapon sheaths. From the Victorian Uniform Guide for one particular unit(all emphasis mine):
Walking Out Belt - A P71 buff leather belt whitened, worn when not on duty.
Another aspect of the 'walking out uniform' was the 'swagger stick' which I encountered while researching another question:
In the British Army before World War I, swagger sticks were carried by all other ranks when off duty, as part of their walking out uniform. The stick took the form of a short cane of polished wood, with an ornamented metal head of regimental pattern.
So, the off duty uniform you could expect to find soldiers wearing, the walking out uniform, would not have included a sheathed bayonet on the belt.