At the moment, part of the town centre Pedestrian Heart is sealed in behind fencing, after the King's Head fire. You may need to change your route through the centre as a result of this.
I've tried drawing this out, but it's an old aerial photo.
I often used to ride up Priestgate, then turn right to get to Bondgate. This is currently blocked, so I either carry my bike up the steps onto High Row, or turn left and use the ramp to get to High Row.
It is possible to get between Northgate and Bondgate, but the gap between the fence and the building is fairly narrow - the width of the 'pavement' style section. It might be worth pushing the bike through here, unless it's very quiet.