Whats the official way buses are supposed to come into Newcastle from the Tyne bridge now, alot of them pull off and go up Pilgrim street while others are still using market street (Both are very slow moving with John Dobson street being closed)

This morning the driver I had decided to continue up the A167 and then came off at Great North Road going past Haymarket then into Eldon Square bus station. At the time I thought he had went the wrong way but the way he went it took about 5 minutes to get from the Tyne Bridge to Eldon Square, where as the other 2 routes take about 15minutes.

To me it makes complete sense to go that way, although it does mean he only stopped once in Newcastle at Eldon, but that doesn't at all bother me. The time it takes to get through the city centre its better just to get off and walk. 

Are certain services supposed to go one way, and other services another?