More speed takes higher voltage (or a motor wound to go fast on lower voltage) to make the motor spin fast enough, and higher power (watts) to overcome the air resistance at the higher speed.
Voltage vs speed is linear, but power vs speed is not, it takes way more power to double your speed than just double the power. At a guess something between 5-10kw of motor power (and because the system is nowhere near 100% efficient, the battery will have to provide even more power than that, by a large margin), depending on how aerodynamic you and the bike are, assuming flat roads and no headwinds. More power will also give you faster acceleration.
How much power you need you can use the simulator at http://ebikes.ca/tools/simulator.html to guesstimate, for the specific conditions you will be riding under. It has instructions and explanations below the graph and tools. It'll probalby take more power than it estimates, since it's designed around bicycles, but if you know the Cd numbers for your bike you can put those in to get closer results.
A new controller is probably needed, and possibly a new motor if you need continuous power well above it's "rating". (motors can often handle a fair bit more than "rated" for short periods, if there's enough cooling they might handle it a long time).
The battery must supply all that power, so if your present battery can only supply the power the present controller can demand, you would need to replace the battery with one that can handle the higher power; this is probably going to be pretty expensive if you need any range out of it.
Additionally, since you'll be using up the power at at least a few times the present rate, even if your present battery will supply that much power, it will give you proportionally less range (so if you get 20 miles out of it now, and it takes 5 times as much power to go the speed you want, you'd only get about 4 miles out of it then).
Another consideration is "how well built is the bike itself?" Is it built well enough to handle the faster speed, on the road conditions you have? Is it's suspension capable of handling it? Are it's brakes and tires able to handle stopping you from that speed? Is the wiring capable of the currents you'll need?
My guess is it could be cheaper to buy a bike that already does what you want than to rebuild this one to do it, but it depends on the compromises you're willing to accept and the reliability and safety you expect from it.
If you look around at the various motorcycle conversion / build threads, there are discussions about power, controllers, batteries, motors, etc., to do faster speeds, that may help you determine what budget range you'll need to expect.
