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I agree that you don't want to be doing the walk from Belfast port into the city centre. Apart from taxis, there is the Translink metro 96 bus, but do check the online timetable as it is a limited service.
In Durham, the first two 265 journeys out of Durham call at Belmont Business Park (handy not only for workplaces there but also for collecting parcels from the Royal Mail delivery office), and two late afternoon 208s call there on their way into Durham.
23 from St Andrews to Stirling which was operated by Stagecoach double deckers and made 4 or 5 return journeys per day Monday to Saturday and took about 3 hours each way.
I used my UK contactless cards on buses/trams in Vienna and Prague this summer without any difficulty, but the systems were not the same as London since in both cases I was effectively buying a ticket from an onboard ticket machine.
I'd buy from the guard and then either go to the ticket office on arrival in London to exchange the paper ticket for a cardboard one, or present my paper ticket at the underground gateline and ask staff there to open the gates for me.
This link suggests that the NS bridge was near Market Rasen, but I have no personal knowledge that enables me to vouch for the accuracy of this:
https://www.geograph.org.uk/photo/3554716
But here's an OS map link (c.1905 from amazing National Library of Scotland site)...
£81 Kings X to Hull Advance (i.e. booked train only) ticket on LNER's 1718 through service arriving 2005 (i.e. 9 minutes later than the connection from the 1703). Or £54 Advance on the 1848 Hull Trains departure arriving 2118.
On the 23rd, £26.75 Hull to Birmingham Advance on the 1727 changing...