imo Haymarket is the least of the issues, what happens if your bus terminates at Eldon Square or Market Street; the walk is even further and there's no sensible way to get between anything. Newcastle has last mile issues all over the place though; the Quayside to Eldon Square/Haymarket being another one and that involves a steep bank.

A better solution that a shuttle bus would be a free city hopper like:


Which connects the major issue points, especially the Quayside imo.