Since then repeated talks between Unite and Arriva have offered up no compromise with the strikes causing significant disruption.
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The union has promised that the strike action will continue 'indefinitely' until an agreement can be reached but speaking exclusively to the YEP, Phil Bown, Unite's regional officer, admitted a deal could now be close.
"We believe there's a deal close. We met with them last Monday and they put the same offer that's been around three times and we told them that wasn't going to wash but we have put two counter offers back to them," he explained.
"We haven't heard back from them since they went away to consider it but we are hopeful of receiving something this week that we can put back to our members."
The strikes began after an Arriva Yorkshire offer of a 4.1 per cent pay increase was described as 'pitiful' compared to the real inflation rate (RPI), which currently stands at 11.1 per cent.
Drivers are looking for an hourly fee of approximately £13.50.
"I would say that we are definitely starting to talk in the right ball park. I obviously can't comment for Arriva but they didn't dismiss the claim we put back to them out of hand and said they would take it away and work up some figures," Mr Bown said.
"We had a speculative call saying that they were hopeful to have something back for us tomorrow so hopefully we will have something then."
The bus provider and union have previously disagreed on the amount being offered after Arriva claimed their original offer stood at between a 7 and 12.5 per cent pay increase rather than the suggested 4.1 per cent.
In a short statement provided to the YEP, a spokesperson, for Arriva confirmed they are hopeful that tomorrow's talks will bring the strike action to an end.
"We’ve opened up a positive dialogue with Unite in Wakefield today which we look forward to continuing tomorrow.
"We very much hope this latest conversation will bring a swift conclusion to the industrial action and a return to service for our customers."
It's now four weeks without Arriva services with Mayor of West Yorkshire, Tracy Brabin, putting in place free shuttle services to Pinderfields Hospital from the centre of Wakefield to try lessen the impact.
Mr Bown admitted his drivers were keen to return to work but that they would not do so until their terms have been met.
"The passengers are not the only ones getting frustrated. My members are also getting frustrated because they want to go back to work but they also want a proper and reasonable rate of pay," he said.
"We thank the passengers for their patience and support. We really do appreciate it but we don't hold the purse strings, Arriva do. They could resolve this all overnight by just meeting the claim."