The problem lies in power to weight ratio of the bike. Bikes that use diesel as fuel are heavy in size. The power output from the diesel engine is high and more over noise and vibrations are at a high level, prohibiting them in common use.
Diesel cannot be used with 50, 100 and 150 cc engines, because of high power output. Diesel engine is a compression ignition engine where diesel injected into a cylinder of high pressure and temperature compressed air, under a very high pressure.
Atomized diesel particles come through a tiny hole of fuel injection nozzle burn and release mechanical power output. Design and manufacturing of such minute mechanical parts, withstanding high temperature and pressure is not cost effective.
And usage of diesel demands heavier construction of all structural parts to endure high vibrations. The cost is also high. If the engine is not serviced properly and periodically the pollutants level emitted will be very high when compared to petrol engines. At present only Enfield India Manufactures motorbikes which use diesel as fuel.