In this day and age the only day when I think buses aren't required at all is Christmas Day. Every other day some sort of bus is required I do believe, Boxing Day is becoming more and more popular just looking at Flickr streams you can see demand is there for certain service and Go North East run commercial services which must make profit despite higher costs to run them.
New Years Day is another one when I do believe Asda supermarkets are open? At least I believe Peterlee/Seaham are. There's also a premier league match at the Stadium of Light yet there's not buses on, you only have to look at how packed the 56 is on a match day!
I think a GNE Boxing Day style service is required on New Years Day. And I think maybe a increased service is required by all operators on Boxing Day. No buses Christmas Day.

I know people will shout and say bus drivers need a rest too, but at the end of the day certain jobs require certain demands. Hospitality, catering, public services are required on bank holidays etc. Certain jobs require a lot of working away, a lot of working from home out of hours and every job is the same.