Are two-way bicycle lanes allowed on highways?

Bicycle lanes are to be located on both sides of the road on two-way streets. Two-way bicycle lanes on one side of the street create hazardous conditions and are not recommended.
Riding a bicycle against the traffic flow is against the law in New York and is discussed
in the Vehicle and Traffic
Law Section 1234(a)
Upon all roadways, any bicycle or in-line skate shall be driven either on a usable bicycle or in-line skate lane or, if a usable bicycle or in-line skate lane has not been provided, near the right-hand curb or edge of the roadway or upon a usable right-hand shoulder in such a manner as to prevent undue interference with the flow of traffic except when preparing for a left turn or when reasonably necessary to avoid conditions that would make it unsafe to continue along near the right-hand curb or edge.

References
Chapter 17. Bicycle Facility Design (pdf)
NYSDOT Highway Design Manual
Lesson 19. Bicycle Lanes (pdf)
FHWA Course on Bicycle and Pedestrian Transportation
NYS Vehicle and Traffic Law: Section 1234
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