I left the following message on the Western Greyhound bus company complaints page last Sunday evening (there are separate fields to identify the time, bus ID, etc.):
"I was riding my bicycle through Hayle along the B3301 at about 15-20mph when I heard a vehicle give a short honk behind me. I looked over my shoulder and saw a green double decker bus and the driver then sounded the horn again. Following this they passed me and then shortly afterwards turned down Lethlean Lane, I followed as I hoped to speak to the driver but then the bus stopped due to traffic and the situation was unsuitable for a conversation, so I passed the bus and carried on my way via Brookway.
Later, at approximately 2.15pm, I was climbing the steep hill on the B3301 up from Godrevy to Hells Mouth, at a slow pace of about 6-8mph, and about two thirds of the way up I was again aware of a large vehicle following, which again gave a single honk of the horn, and then after I had looked over my shoulder again honked a second time. Yet again the bus was able to pass shortly after as the road widened. It was the same bus on both occasions, and I made a mental note of the registration number then recorded it on my mobile phone when I stopped at the top of the hill shortly after the second incident.
I am not sure why the driver felt the need to use the horn at all, and particularly for the second time on both occasions after I had looked round, when my riding position was 'by the book' throughout at about a metre from the kerb, what is known as 'secondary position', and besides which a bus driver's opinion of a cyclist's position does not give them the right to use the horn aggressively, see highway code rule 112.
I feel I should have an explanation and apology from the bus driver concerned, as it is very intimidating having someone drive a double decker bus close behind you sounding their horn at you repeatedly in an aggressive manner, though at least the passes had been satisfactory."
I received a letter in reply later in the week, in which, after some preliminaries about taking complaints seriously and training drivers to high standards, the explanation offered was that "after a previous incident which has made her nervous, our driver was simply being cautious and tried to make sure that you were aware that she was driving behind you. She did not mean for this to come across as being rude, and conveys her apologies if this is the way it seemed."
I shall maybe write back and suggest she does not continue beeping once a cyclist has very obviously turned round and clocked the big green bus behind them.
In general a car beeping behind is a sign that my road positioning has been effective, they have seen me and are objecting to me taking my rightful place on the road instead of the gutter and/or I have succeeded in stopping a risky overtake at a pinch point. There is, as pointed out, the danger of a 'punishment' close overtake following later, but that is relatively uncommon IME.