The inquiry will take place after objections were made against the compulsory purchase orders which were needed to for the 3.3 mile stretch of road.
The Bedale, Aiskew and Leeming Bar bypass will take the main A684 road into the Dales out of the town and through open countryside with three roundabouts, two bridges and extensive embankments.
The road will rejoin the A684 between the existing entrance to Bedale golf club and the town's sports club.
For 20 years, North Yorkshire County Council has been pushing to build the road, and the proposal is supported by Hambleton District Council, Bedale Town Council and other nearby parishes.
The road is expected to halve the numbers of vehicles going through the town from 14,000 a day to 7,000.
Work to upgrade the A1 to Leeming Bar to motorway paved the way for the bypass, but the Government has said it will only pay £36m towards it, with North Yorkshire County Council footing the rest of the bill.
County Councillor Gareth Dadd, executive member for highways, said: "We had factored time in for an inquiry, I can’t see it putting the scheme in jeopardy, there may well have been objections from landowners, it was what we expected."
County Councillor Carl Les, said:”This is part of the democratic process and it is a chance for people to air their views.
"It is held by an independent planning inspector and anyone can come as long as they register beforehand, although the inspector will be ruling on the compulsory purchase orders and the side road orders.”
The inquiry will be held at Leeming Lodge on May 21 and is expected to take four days.
Works is due to start on the bypass in autumn 2014 and will take two years to complete.