Yep,
Doubling the speed increases drag, theoretically by a factor of 4, which is where I got confused with my figures, but you are right according to physics, doubling the speed of a vehicle will take the cubed root, 2 x 2 x 2 = 8 times or an 800% increase in power, however, it doesn't quite work out like that, say 25 bhp motorcycle gave you 80 mph, in theory then to do 160 mph you would need 200 bhp! So something else must come into play than just drag co-efficients.
8 times the power to double the speed, due entirely to air resistance, is actually a pretty good basepoint for these things.
It takes about 10 hp to do 60 mph, and the first 20 or 30 mph don't really count in the wind resistance stakes - so just 3 hp will do 40 mph. And a healthy 30 bhp to do 100 mph.
A 55 hp Vincent does 125 mph, so to do 250 mph it would need 440 bhp. Which is obviously off the planet, but so is a 250 mph naked Vincent. Rollie Free with his bathing suit showed there is more to life than horsepower though.
Once you add a full fairing, things improve - and a Honda MotoGP bike with pneumatic valve springs making 270 bhp @ 19,000 rpm gets about 345 kph on the longest straight in MotoGP - thats approx 215 mph.
The Aprilia 250 GP bikes are currently getting ~440 bhp/litre, so a 1000cc version of one, if that were possible, should get that 250 mph easily. Except that this year is the last year for them, next year they go 4 stroke Moto3 spec.
And the Gatsos get ya if you wind it on in 3rd gear. Or even 2nd...
Cheers.