Airport Customs Help & Airport Bus

I have to take the Airport Limosine Bus to my hotel. I arrive in Tokyo on a Sunday at 3:00 and the bus leaves at 5:00 PM. Will I make it in time? How long is the customs process arriving from the United States?
Also does anyone know what terminal United flies into?

It is immigration rather than customs that can take some time. Most of the time, however, it does not take more than an hour from the arrival of the plane until you passed immigration and customs. So, unless you flight is delayed, I think you will make your bus without problems.

United's gates are in Terminal 1. After deplaning, you need to go through Immigration, Luggage Claim followed by Customs before exiting into the Arrival Hall. Directly across you'll see the orange Limousine Bus counter where you can purchase your bus ticket. Exiting through the doors on the left or right will take you to curbside where you'll find the Limousine Bus stop.

Air arrival time is generally when the airplane touch down on the tarmac landing strip followed by about 5 minutes to taxi to the gate. So, it should take you a little over 10 minutes from touch down to arrival at Immigration. The slower process is with Immigration and this is the unpredictable time depending on if other planes arrived at the same time. By the time you get to the luggage carousel, your luggage should be there. Clearing Customs takes only a few seconds unless they decide to search your luggage.

It should take you no longer than 1 hour 15 minutes from touch down to the Limousine Bus counter. So, you should be able to catch the 5:00PM bus provided your plane arrives on schedule.

As a thought: I would recommend you take the door to the right to get the bus: you'll get on first and grab a front seat so you can see the sights on the way in: Japan drives on the LEFT so beware!