I going to preface my response and without doxxing myself...
I was born, raised and educated, and my knowledge of buses was based this very corner of North Yorkshire. My family are still there - some of them have even worked in that Tesco in Catterick Garrison. My parents ashes are scattered above Preston under Scar. I know the area really well... I know the history of those bus services and most importantly, I know where people travel from and to, and why, and how it has changed (or hasn't) over the years. You - less so...
Cost. Running a bus as big as an Evora empty at the start/end of the day is costly. As for what Richmond has to offer, Richmond and Catterick Garrison has everything Northallerton does apart from a train station. Connections onto the X26/X27 from the 159 in Richmond aren't great. Either you improve connections between the 155 & 73 in Bedale or between the 159 & X26/X27 in Richmond to make travelling from Leyburn to a train station easier. Its all about better integration between bus services and onto other modes of transport like rail. That's the point I'm trying to get at.
The 159 is a much busier service than the 155 and is attached to school workings that are also busier. The 159 actually carries some decent loads, especially on Ripon market days.
The 155 simply doesn't and never has done
Connections from the 159 aren't great because, and this might be hard to believe, most people travelling from Leyburn aren't going to Darlington. They're going to Richmond. For the few passengers who do want to travel between the two, it was less of an issue when the service was every 20 mins (and before that, every 15 mins)
Also, I don't know where you get this belief that there's some market for people needing to go from Leyburn to get a train. I suggest you travel on the X26/X27 and see how many people get on/off at Darlington rail station - it is very few (except for a Friday afternoon and a Sunday night) even with a direct service and through ticketing.
So what's your solution? Leave the situation as is which is inadequate? I have provided a road map for improvements with the trial of connections in Bedale is low cost and low risk. You have offered no solution and seem happy with the current provision which lacks integration...
You seem to think that the 155 is inadequate.
Put bluntly, a better service was provided for several years and no b*gger used it. The 155 meets what little traffic there was.
You can put on as many buses as you like between Bedale and Leyburn but the number of passengers would barely change - it simply isn't the money.
When the service actually existed, next to no-one used it, which is why it was reduced even before austerity.
Change the 155 times by all means to connect with the 73 - fine. Your original proposal was an extra £250k p.a. - that isn't low cost.
I do go up to Wensleydale during the Winter, I catch the 856 as the 73/155/156 connection on a Monday-Saturday is a pain. The 856 remains relatively popular because it is the easiest way to travel around the area. There are people who use it during the winter, otherwise it wouldn't run during the winter!
As for a last bus, trialling a later bus on the 155 after the afternoon school journey could be a possibility. Yes, there would be increased costs to do so, of course there would be. Trial connections with the 73 in Bedale first and then look at later buses on the 155. That's a plan for improvements. There's no loss in connecting the 155 & 73 and it has the potential for improvements in the future should they be justified.
There are people but it is much reduced in winter.
Looking at the 2001 & 2021 Census, the population of Leyburn has remained relatively stable just under 2000, not decreasing.
Again - read what I said. I said Richmondshire so that encompasses not just Leyburn but the rest of the area so places on the 155 route like Hunton and Spennithorne and Patrick Brompton. However, as you say Leyburn has remained relatively stable... so why would there be more people wanting to travel now than there were in 2001.
Surely any positive changes in demographics and patronage would also have led to issues with capacity on LWB routes... they haven't though, have they?
I've said this before, these places would be higher up on the list than Leyburn but it doesn't mean Leyburn shouldn't be on that list as you seem to think...
Leyburn is tiny. In terms of population, it is less than a third of the size of places like Pickering, and a fifth the size of Richmond. For crying out loud, it is smaller than Catterick Village.
There are literally dozens of places in North Yorkshire that need better bus services, and much more deserving cases. If we had £40m to spend, fair enough. However and getting back on topic, the idea that there's a load of funding to be released from central government, a reprioritisation of existing spend, or some utopia of franchising and cross subsidy is simply unrealistic.
On paper it looks like a great potential service. The bus service is only 3x a day, perhaps that reflects the demand or perhaps it reflects the operational circumstances of interworking with a school service and the 54. It likely sits somewhere in between. As you say, there's more in Darlington for those in Richmond and Catterick Garrison, and they have a much better bus service to reflect that.
You could theoretically alternate between the 54 & 55 for Richmond-Northallerton. This would require an extra vehicle with the current bus used on the service working a school service. Kirkby Fleetham currently has buses to Northallerton which has everything that Richmond and Catterick Garrison has to offer plus a train station. Would Kirkby Fleetham benefit from a service to Richmond & Catterick Garrison though?
And that's the point - on paper. The reality is that the old 54 (and before that 34) were two separate services/passenger flows and the numbers travelling south of Catterick were pretty low. There used to be the odd passenger that would travel from Catterick or Colburn but it was minimal.
What little Richmond to Northallerton traffic is absorbed by the 55.
Why would Kirkby Fleetham, Great Langton or Scruton inhabitants want to travel to Catterick Garrison or Richmond? There's nothing there that they can't access in Northallerton.