The duration of commute refers to the time it takes from your home to the workplace in normal conditions without extra detours.
Calculate the duration of commute according to the fastest means of transportation at your disposal. Buying a car is not required, but if you have a car at your disposal, the duration of commute will be determined according to that. If you use public transportation, you can include the time spent changing transportation with the waiting times.
As the purpose of mobility allowance is to encourage accepting employment, the allowance will not be cut off even if the duration of commute shortens during the employment.