Im going to assume that you are absolutely sure that the airport limousine bus is what you want. Because there are 4 other public transport options : JR NE’X, JR Sobu, Keisei local, Keisei Skyliner.
First, forget about Expedia. Buy direct. If I take the bus, I buy the ticket on the airport limo website the moment I land, while taxing to gate. That way I’m sure what time. You can do this only if it is at least 25 minutes before bus leaves. But do it only if you are sure you can get through quickly. I can get curbside in 15-20 minutes at NRT, KIX or HND because I have an APEC card and never have checked luggage. The immigration lines are sometimes very long at NRT and HND. But by buying direct, they let you move your ticket 3 times if you miss the bus. ( and there are multiple bus routes you can use as an alternative)
If you don’t want to deal with this uncertainty, buy only after you clear immigration and customs and go the the counter. I have never seen long lines at the counter. That way, you can ask about alternative routes unless you are familiar with where you want to go. I myself have the timetables saved on my phone since I’m there several times a year.
For me, it all depends on the destination and then maybe cost when I choose bus or train. The Skyliner is half the price for example but then you got to add the metro fare to it etc. I use hyperdia or google maps is also good these days.
