There is an pedestrian route to the back entrance of the hospital from Knaresborough Road so from the bus station it is a Transdev 1A / 1B or 1C which combined run every 7 minutes or a Connexions X1 (every 15 min) or X1C (every half hour) during Mon-Sat daytime. Only Transdev run in the evenings and Sundays and at a reduced frequency. The stop for the hospital is Granby Corner, the first after Empress Roundabout (A59/A661 junction). The pedestrian route is not however particular well signed but you would be pretty unlucky not to find someone else making the same journey.
One thing to note is that both Transdev and Connexions are laying claim to the Harrogate Bus Company name so both have vehicles with that on them. Transdevs are done as a proper paint job and they have sought a trademark registration which seems to have got held up due to Connexions registering the Company name to themselves. Transdev buses are usually red, Connexions usually Green and white (although a red West Yorkshire heritage bus and a blue and white Harrogate Independent Travel heritage bus are commonly used on the X1 and X1C) and a few have the Bus co name above the front door / driver window in blue lettering with an exclamation mark after it.
Three other operators regularly run into the town - The Keighley Bus Company (Transdev in Keighley) on the 62 from Keighley via Ilkley and Otley, Transdev York on the "Little Explorer" 22/ 23 from York via Ripon and Knaresborough and Yorkshire Tiger with the 747 from Bradford via Leeds Bradford Airport. The 62 is shown on the Transdev Harrogate Bus website so Transdev Harrogate fare offers presumably apply to it but not to the "Little Explorer" worked by Transdev York.
There is a "Daytripper" ticket which allows you travel on all Transdev buses across Yorkshire and Lancashire
http://harrogatebus.co.uk/fares/TheHarrogateBusCompany/Daytripperticket_115.html
"Where will your Daytripper take you? Our network wide ticket means you can travel on any Transdev bus in Yorkshire, Lancashire and Manchester. Shopping, sightseeing, hiking from city to town to countryside with no boundaries; you asked, and now we can take you there. You can be a lone ranger or save as a group of up to 5 adults.
Daytripper is valid for travel as far east as York on Coastliner, but not including onward long-distance travel to Whitby, Scarborough and Bridlington is £9 for an adult; £6 for children and £19 for a group of up to 5 adults.
Daytripper Plus includes full access to the coast on Coastliner as well as including the open-top York City Sightseeing bus travel. A Daytripper Plus ticket is priced at £15 for an adult; £10 for a child, and £31 for a group of up to 5 adults."
but should be noted that Transdev Keighley have a bargain day ticket
http://www.keighleybus.co.uk/fares/TheKeighleyBusCompany/DayPeriodAnd12-journeyTickets_23.html
"A K DAY ticket costs just £4.20 (£4.90 before 0930 on Mondays to Fridays).
K DAY is valid throughout on theSHUTTLE into Bradford, the 760 into Leeds, the 62 to Harrogate, and many more. You can also use a K DAY on Mainline between Keighley and Colne, and between Skipton and Barnoldswick. K DAY Tickets are not valid on DalesBus 872"
This K day ticket significantly undercuts Connexions fares on their competing X52 from Ilkley.
