How about early/mid September - 6/7th, 13/14th, or 20/21st (said without looking at a calendar to see what other events are on around then). Alternatively we could look at something in July. I thin August is probably out for a few of the likely contenders because of holidays, birthday rides etc. I think it's going to take me until then to remember what order we did all the bridges in to end up crossing each one in the right direction.
I assume that we are aiming for the following crossings again:
Tyne Tunnel, Shields Ferry, Millennium (Blinking Eye) Bridge, Tyne Bridge, Swing Bridge and the High Level. Redheugh Bridge is a bit pants and I don't think people would be happy if we went for the rail only bridges. If we did Redheugh we would then need to get down to Blaydon Bridge (need an even number of crossings to end up on the same side of the river you started from...). We should also aim to actually get as far as the lighthouse this time and not be diverted by the ice cream van...