If you have your own car and driver it is pretty straight forward for them to drive through, we do it all the time. With a car there are about 4 windows you need to get checked at but at Cyanika (quieter border) it is pretty straight forward and the driver will do all this. I don't know where you're staying in the forest but the 90 mins is from the southern edge, so if you have the same driver or a new driver meet you at Cyanika the time it will take will be 90 30 + 45 120 = nearly 5 hours.
To save a bit of time you could drive to Kisoro after your gorilla trek, stay O/N at Travellers Rest and then hit the border first thing in the morning when it opens. Kisoro is literally 5-6 miles from Cyanika on a good road.