國光客運-國光號[1819路 往台北車站
I highlighted for you. 台北車站 is opposite 西门町 but depending on your luggage it can be pain in the ass to walk across huge bridges etc, long winded. I did it before with 3 heavy bags, sweat even in winter KNN!
Oh! I forgot! That was long ago before they got 捷运 when I walked. Now there is train to take from 台北车站 to 西门站。Just one stop, depending on your destination that one stop may slightly overshot. Then you back-track a bit.