Since no one rose to yesterday's challenge I have done some research myself. The Shorelink service 44 is operated by Centrebus on behalf of Rutland County Council. The vehicle used is Dennis Enviro 200 YX13 EJA, new in June 2013, reduced to 34 seats to accommodate bikes, and given fleet number 501. As yet I'm not sure which depot she is based at or what used to operate the service.
I also found a video promoting the bus on the Rutland Council website, which can be viewed by clicking the link below.