Well, we're often told on these pages things along the lines of, "this route can barely support a bus service so a railway has no chance", so it stands to reason that if the bus does well, it could point to the need for a fixed link.
Unless it's a case of the anti-rail brigade trying to have it both ways.
Remember that patronage is only 1 side of a rail case.
I agree with you that a well-loaded bus link will
help the rail case. However it will not do anything material towards
proving it. A bus is, by definition, much lower capacity but this is balanced by it's much lower costs. At the moment the bus service in rail journey planners is every half hour, and a bus takes 40-50 people, or approximately 1/2-2/3rds of a single rail carriage. A single rail car shuttling up and down the branch every half hour will need the absolute cheapest costs.
Now for a bit of feasibility. A route broadly following the A66 is c.15 miles, and to keep costs down we'll go with a target speed of 60mph. That gives a flat-out journey time of 15 minutes, plus 1 minute at either end for acceleration/deceleration, so 17 minutes. As it's a short journey and train we'll assume a 3 minute turnround at Keswick is feasible. That gives 17+3+17 - 37 minutes between wheels start and wheels stop at Penrith. So we need a 2nd unit
and loop/platform on the branch. This massively increases the infrastructure costs as you now can't just have a single axle counter at the top of the branch and One Train in Section. It also increases crew and unit running costs.
You could reduce the service to hourly - this would certainly allow a simple single-track with plenty of room at Penrith for connections. This would be balanced with the reduced journey opportunities as connections are longer and the service itself less frequent. This is a classic line where if it had never closed, it'd be getting an hourly service trundling on unable to be improved or removed. However given the season nature of the traffic, 1tph with the additional buses in high traffic period might well be sufficient for what the line is meant to do.
For reference, to go the other way - to achieve a reliable 2tph service with a single unit you'll want 10 minutes turnround between the two termini (3 minutes at Keswick might be viable but you don't want every train on minimum margins, if you're extending other services down the branch you'll want about 10 at Keswick to provide resilience), so you have 10 minutes for the journey each way. Remembering we're adding a minute for acceleration and braking at each end, that's a journey of 15 miles in 8 minutes, which is 112.5mph. Of course, the higher your top speed the longer you'll spend accelerating and braking so we're now talking a 125mph railway, defeating the point of 'low cost'.