Controllers have capacitors inside them and they have a certain voltage rating. On many cheap scooter controllers rated at 36 volts the capacitors are rated at 60 volts so you can run them at 48 volts without any problems.
What you need to do is find out what capacitor ratings your capacitors have to know. If you can take it apart and look you will be able to make the decision.
As for the motor...
Motors subjected to higher voltage will get hotter, so you also need to worry about overheating with a voltage upgrade. A lot of people do it (I do) but you need to know what you are doing.
When you upgrade from 36 volts to 48 volts you will get 4/3 the power and 4/3 the speed. The higher rpms will not harm the motor because at high rpm the motor is under less load. What you need to be VERY CAREFUL about is using too much throttle when you are at low rpms. An example is a very steep hill where the bike wants to bog down... if you hold full throttle on that it will heat the motor up and could cause failure.
So just "baby" the low end a little until you are sure of what it can take. The best power is at about 80% of max speed.
Be careful of everything below 50% max speed.
The first thing you should do is get onto a straight away and find out what the top speed is. Let's say it's 30 mph. So we have:
0 - 15 mph : Be careful with the throttle
15 - 30 mph : Wide open is just fine
...I have a six speed transmission on my old bike and I know all my shift points, but with a one speed you just need to pedal below 50% or use less throttle.