If you get stuck in traffic -meaning any rush hour, say 7am or 7pm flights- it can take up to two hours. Once I had a poor pal planted like a tree at Taoyuan because I took the hotel bus. Another time thank goodness I had taken a limo because the guy just dropped out of the highway -after some McGiver moves- and into some backroads, otherwise I wouldn't have caught my flight -I am talking about stretching for miles on end, 5kms an hour, bumper to bumper. Bus also has for me the disadvantage of losing sight of your luggage... which might be permanent.
MRT takes all the guesswork out. Point to point, time allotted is time assured. Bags on sight at all times.
That is the beauty of Songshan, even with the Brown line transfer. Smooth, easy. I am not sure the line to Taoyuan Airport will be that fast as desired, but it will be a fixed time.