This might be a medical issue - as the scooter is motorised, its clearly not the physical effort making you tired. There is mental effort, negotiating traffic on the way, but that wouldn't really explain your tiredness UNLESS you find the drive terrifying or it makes you feel panicked or very stressed every time. That would cause fatigue. Not sure how you could reduce your anxiety about the journey other than simply becoming accustomed to it over time.
If you're fatigued after the journey home as well as the journey to work, and the journey is always in heavy traffic, the next likeliest explanation is your intake of pollutants in the air on the journey. Even persons driving a car with the windows closed show high levels of pollutants in their blood after a 20 minute drive, mostly caused by all the traffic on the roads. Sensitive individuals may respond to air borne pollutants by unconsciously hyperventilating, and that alone can make a person feel tired, never mind the effort the body has to go to try to deal with the toxins in the system. In which case, I suggest you do some research and find a suitable and efficient mask you can wear to reduce or minimize the amount of fumes and pollutants you're breathing in to see if that helps.
The link below is for a pollution mask favoured by some cyclists in London, no idea if you can get it where you are, but its more comfortable to wear than most and fits better on female faces:
Respro is another brand much more commonly used though I can't speak for the efficacy of either of these.
If, though, you experience this fatigue at other times when you're not riding your scooter, a visit to the doctor is probably called for to eliminate other possible, health related reasons.