Indeed, there is a shuttle bus that runs every hour, on the hour, I'm not sure when service stops. At check-in, the receptionist asked if the bus was needed and my departure time. It was suggested that I make a reservation, though not required. The Taoyuan MRT is also an option if it suits your schedule; it is just a stop or two away, depending on which terminal.
I was advised, that walking is not an option.