Increase The Speed On An Electric Bike

Update:27 Jun 2019
Summary:

There are two venues for making a vehicle faster. More […]

There are two venues for making a vehicle faster.

More power: In electrical terms, power=voltage*current.

Use a motor that's rated to handle higher voltage or current will be able to convert more electrical energy to mechanical energy before catching fire.
Use batteries that can supply more current (lithium-polymer, instead of lead-acid, as an example). Connect them end-to-end (in series) to increase voltage.
Use a solid-state power system to reduce energy being turned into heat before it gets to the motor.

Use the power more effectively: Go lighter, sleeker, smoother.

Change the gearing to take advantage of the motor's performance characteristics.
Reduce weight by removing unneeded parts, replace metal with composites, etc.
Reduce losses to wind resistance/drag by improving the aerodynamic design of the vehicle.
Reduce or eliminate friction in the drive system by using better lubricants, replacing metal bearings with ceramic, and moving to direct-drive.

A combination of the two will result in the "best" solution.