The exit slip is defined as a "bus gate" in the
TRO -
1. Tyne Bridge Slip Road southbound entry slip (offside lane) -from Pilgrim Street Roundabout for its entire length
. You've quoted the section of the TRO for the bus lane on the opposite slip road leaving the Tyne bridge, not joining the road. Looking at the road layout, this appears to be correct as it's a separate carriageway at the point of leaving the roundabout - so I don't think the location argument assists here (the bus slip road doesn't appear on street data). Others may disagree however.
Regardless, "Tyne Bridge Slip Road" seems like an accurate description of the location, and it's defined as coming off the relevant roundabout, so I think you'll struggle with a locational based arguement.
As per usual advice, please post the PCN in full.