The decision was taken behind closed doors by Hambleton District Council’s Cabinet who excluded the press and public as they discussed the cost of buying the land for the scheme on the outskirts of the town.
The three mile long road which will take vehicles around the north of the town, also bypassing Aiskew and Leeming Bar, is due to be built by North Yorkshire County Council, with contributions from the government, at a cost of £42.5m.
But they will not pick up the cost of the gateway car park, which is seen as Hambleton’s responsibility and has always been regarded as a crucial part of the plan by people in Bedale to ensure visitors and tourists do not bypass the town.
It is not known how much the car park will cost but it is thought to be far more than the original estimates of £100,000.
Bedale councillor John Noone said he could not comment on the confidential aspects of the scheme but said the car park was vital to the town.
“The benefits the relief road will bring would be hugely damaged if people didn’t have chance to park and come into the town for shopping and to visit the cafes, restaurants and pubs," he said.
“The bypass would become a bit of a liability without it because while it would relieve the traffic around Leeming Bar, Aiskew and Bedale it would funnel the traffic around the town on the road to Leyburn.
"We want to take advantage of the big opportunities for tourism and shopping that Bedale can offer."
Work on the new bypass is due to start this summer, if final costings are approved.
It will take the main A684 road into the Dales around the town.
The bypass will leave the road from Northallerton before Leeming Bar and rejoin the road to Leyburn just opposite Bedale golf club, where it is understood the new car park will be built on the same side as the existing Bedale sports club.