The elderly man's son, Wayne, claims he was forced to stand in front of the bus and wave at it to stop - only for the driver to respond by swearing and abusing the five paramedics.
The 43-year-old said: "He should have had more respect for the ambulance crew.
"They were just doing their job. God forbid he ever needs an ambulance. What if it had been one of his parents?
"Would he have liked it if someone hurled abuse then? He should be named and shamed."
Arriva has since issued a statement in which it apologised to the May family and said a full investigation would be carried out.
The emergency teams had been called to Mr May's home - where he lives with his wife Maureen, 62, and another son - after he fell out of bed on Tuesday morning.
As well as open wounds on his head, it was suspected he may have suffered a broken shoulder.
The first crew called a second vehicle for assistance and then a third with specialist lifting equipment was requested.
All three were parked along the single carriageway when the alleged incident occurred at 7.45am.
Mr May, who runs Artisan Rare-breeds in Dartford, said: "The ambulance crews had stopped the traffic both ways. Other motorists in cars and lorries all stopped but the bus driver just kept edging towards me.
"I had to stand in front of it and wave my hands to make it stop. I could see the driver was hurling abuse. Then he opened the door and I said: 'What's your problem?'
"He was swearing, but rather than lose my temper with him we just had to get my dad sorted."
Mr May said the bus driver's reaction was in stark contrast to that of other motorists who had been made to stop.
"About 11 people slowed down as they eventually drove past and asked whether he was my dad and if he was OK or saying they hoped he was OK," he said.
Mr May senior was taken to Darent Valley Hospital but was later discharged, having suffered just bruises and cuts to his face.
Mr May said he could not say how many passengers were on the bus, but noted that its destination was Ebbsfleet Academy in Swanscombe.
Concerned by the driver's reaction, he reported the incident to both police and Arriva.
A police spokesman said they had received a report of bad driving, but said ambulance crews did not have a right to close roads or direct traffic.
Arriva said the driver has been identified and interviewed.
A spokesman said: "Arriva expect all their drivers to be courteous and polite at all times and show patience in a situation like this. We will be investigating the matter in full and we would like to pass on our apologies to the family during what was clearly a distressing time."
South East Coast Ambulance Service said nothing was recorded on its log, but added: "We would ask motorists to be understanding and patient if an ambulance is causing an obstructing."
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