Night shift worker Christopher Taylor, 58, was initially charged with causing 82-year-old great-grandmother Patricia Taylor's death by careless driving, but the charges were later dropped, Wakefield Coroner's Court was told.
The inquest was told Mr Taylor, who is not related to Patricia Taylor, was suffering from undiagnosed sleep disorder obstructive sleep apnea when the collision happened just after 8.30am on Saturday November 17 2015.
The hearing was told "fiercely independent" widow Mrs Taylor, who had worked as a domestic supervisor at St James's Hospital for 40 years, was stood at a bus stop on the A63 Selby Road at Cliff Top, Garforth, when a VW Polo crashed into the shelter and struck her.
Mrs Taylor, from Garforth, suffered serious multiple injuries and died at Leeds General Infirmary ten days later.
Christopher Taylor, who told the hearing that at the time he worked night shifts from 9.30pm to 7am and had been working the night before the collision.
Mr Taylor said: "I recall driving at around 30mph about a quarter of a mile from the accident and from that point I don't recall driving until the bus stop started showering down on me.
"I would like to express my sincere sympathy to Patricia Taylor's family. I really am sorry."
The inquest was told Mr Taylor was suffering from stress after the collision and went to see his GP, who thought he might be suffering from obstructive sleep apnea.
The inquest heard two medical experts later agreed Mr Taylor was suffering from the unrecognised and untreated sleep disorder.
Sgt Carl Quinn, of West Yorkshire Police's major collision enquiry team, told the inquest: "All the facts do support the consideration given by the experts that Mr Taylor may have fallen asleep."
Sgt Quinn said Mr Taylor was charged with causing death by careless driving but the Crown Prosecution Service offered no evidence at court and the charges were dropped.
The inquest heard Mrs Taylor died from acute pneumonia due to multiple injuries.
Area coroner Jonathan Leach recorded a verdict that Mrs Taylor died as a result of a road traffic collision.
In a statement she read out at the hearing, Mrs Taylor's daughter Beverley Wray wrote: "My mum Patricia Taylor was fiercely independent and people never believed she was 82.
"She has left a big gap in all our lives. I am devastated and find it hard to even function most days without her.
"Each day now starts with a trip to the cemetery. I have never been out anywhere without my mum, I feel so lost without her."
She added: " I could have accepted mum going peacefully, but she had terrible injuries and was taken from us so tragically and so sudden, when she had so much more to live for."