That is an excellent observation. If he had specifically wanted the 23, he could have caught it from outside his front door. By walking along Kensal Road as far as the bus stop on Ladbroke Grove, he gave himself the option also of catching any of the 52, 70, 228, 295, 316 or 452.
Buses nearby Kensal House
So where do their routes intersect with the route of the bus he did get on?
Well, the 23 goes to Ladbroke Road tube, then via Portobello Road, Westbourne Grove, Queensway, Paddington, Marble Arch, Park Lane, Hyde Park Corner, Knightsbridge, High St Ken and Olympia to Hammersmith.
The 52 follows the same route to Ladbroke Grove then takes a different route but intersects the 23 route at Knightsbridge and Hyde Park Corner before going on to Victoria.
The 70 takes a completely different route but does go to Hammersmith Hospital before heading further west to Acton and Chiswick.
The 228 goes to Ladbroke Grove tube but then heads out to White City, Acton, Willesden and Harlesden before terminating at the Central Middlesex Hospital.
The 295 also goes via Hammersmith and stops at Charing X Hospital before going south to Fulham and Clapham.
The 316 goes to Shepherd's Bush.
The 452 heads down Ladbroke Grove to the tube station, then intersects the 23 route at Kensington and Knightsbridge before heading south to Wandsworth and Vauxhall.
It's possible he wanted a choice of buses heading directly down the hill to Ladbroke Road tube, I suppose. It's an easy walk for an able bodied youngster. But we know that Richard isn't completely well. If he was in pain, he might have taken the bus to get to the tube, and after that anything's possible.
If he stayed on the bus, though, my best guess is that he was heading for the Hammersmith area, as three of the buses from the bus stop he walked all the way along Kensal Road to get to go there. The only other intersection points with the 23's route are Knightsbridge/Kensington/Hyde Park - possible, but hard to see what the specific draw would be at 9'oclock on a Monday night.
The other thing that occurs to me is whether he was heading for a hospital. St Mary's in Paddington and Charing Cross both have A&Es. Hammersmith doesn't, but he may not know that - and I think it may be the hospital he's used to going to for haematology services. St Mary's is in the same healthcare trust and would probably be the one he's advised go to for help related to his condition out of hours.
Can the CCTV WebSleuthers manage to pull up any images of the 23 arriving at St Mary's Paddington about 15 minutes after he got on to it and/or Hammersmith Hospital an hour later?