In the US, the designation "Bike Route" is a Department of Transportation term used for planning and engineering purposes only.
It means that bicycles as a form of transportation needs to be considered whenever a roadway is maintained or improved. It does not mean that the road is bicycle friendly. suitable for cycling or a that it is a good place to ride.
The "Bike Route Ends" sign simply means that traffic engineers and maintenance crews can ignore bicycles as a form of transportation for the section of road beyond the sign.
-Tim-