Kirkby Lonsdale Coach Hire (KLCH) launched its Craven Connection service last week following a strong campaign to get a full service re-started following the collapse earlier this year of Pennine Motors.
Colin Speakman, a member of Dales Bus, said passenger numbers were well up and even exceeding expectations.
"The service is going splendidly, but as with any new service, there have been one or two teething problems," he said.
That included a driver misreading a schedule, and leaving passengers behind, and destination blinds not showing the right destination.
"The company would like to apologise to anyone who suffered any inconvenience," he said.
There has also been an issue with the moving of the bus stop in Giggleswick from the centre of the village to Four Lane Ends.
Concerns have been raised that more elderly and less able bus passengers are now faced with a long and potentially dangerous walk to the re-located bus stop.
But a spokesman for North Yorkshire County Council said the council was aware of the problems and was working to come up with a solution.
Mr Speakman added there had been a very warm welcome to the new service.
"The fact that passengers wanting to travel between Kirkby Lonsdale or Ingleton and Skipton no longer have to change buses at Settle has been very much appreciated, and walkers are finding it a very good way to reach Ingleborough."
Meanwhile, bus users in Carleton are holding a public meeting on Tuesday (Aug 12) to express their anger at the reduction of services to the village. Council mini-buses are operating services in Carleton, in addition to Embsay and Horse Close, Skipton, but there are only three buses a day to mCarleton - because the council says demand is low compared to other places.
Steve Richardson, of the Carleton Save Our Bus Campaign, said: "There is a lot of anger and frustration in the village, and to organise this into a unified response to the council and to let them know the true weight of opinion and the hardship this is causing, there will b e a meeting to allow the community to register its feelings and to help co-ordinate a village wide response."
Tuesday's meeting will take place at Carleton Village Hall at 6.30pm.