At 6:25 and travelling away from Tokyo I wouldn't anticipate a lot of traffic.

The limobus only needs to navigate a few potentially busy streets before it hits the Bay area and its expressways. I would expect the journey on this particular route to take no longer than 1 hour 15 minutes (1 and a half hours maximum). I'd say an hour, but you may have to pick up some passengers at other hotels first.

If you were travelling later in the day or on a different day of the week or joining the bus in a different area I'd join you in your caution, but I seriously doubt that the 6:25 bus will arrive later than 7:45am.

And Sunday makes a huge difference - last time I got a bus (not the limobus) was from Shinjuku, on the other side of Tokyo, on a Sunday. We got to Narita in an hour and 2 minutes.

And you won't have to book the bus into Tokyo. Just turn up at the dedicated Limousine Bus counter, buy your ticket and board.