Gregory's Server@Arthurian That's not a problem with public transport as such, but with badly designed (hospital end) and too little (where you are starting from) public transport.
A hospital should be well connected to large transit lines, like one or more metro lines, light rail, MTR. Situated at/over the station, with short, accessible walkways. And wherever you are needs to be close to some kind of transit that will bring you to your closest hospital with a minimal number of changes. It's not hard to design, but it needs to be built and run.