Greyhound does have restrooms in the bus. However, do you know for certain that it will be a Greyhound bus and not a subcontracted bus? The other companies do not always provide the same quality as Greyhound.
If you have to switch to a different brand bus during the journey, the other company may not provide one. Years ago, I bought Greyhound bus tickets from Roseburg to Bend. The trip was roughly half a day. The first half of the trip was on a Greyhound bus. Once I arrived in Eugene, I had to transfer to a smaller company bus to go through the Cascade Mountains into Bend. This bus was only a 15 passenger short bus and had no such facility.
Another question is how much you despise unclean restrooms. Greyhound does not have the same cleaning policy as more expensive options. The few times that I have traveled by bus, I was disappointed by the cleanliness. Some people have difficulty using stationary toilets. One installed in a moving vehicle is even more problematic. Nothing like a pothole or expansion gap to upset one's aim.
IMHO, wearing a diaper is the best option. Not only is it more sanitary, the waiting line will always be shorter. Either way you choose, have anti-bacterial wipes (Wet Ones or baby wipes) and waterless hand sanitizer (Purel) in your carry-on luggage.
Diaper, unless you are uncomfortable going in front of other people. For me, when I am around others (like at lunch at school) I cant get a drop out. So, I would go with either hand-sanitizer and wet-ones (because they don't have any smell), or diapers and wipes and powder.
I've had good experience going diapered on Greyhound. It's one of the few good things about those trips. Greyhound is an awful way to travel, but its saving grace is that it's still pretty cheap. I'll be taking it next week. And yeah, I'll be diapered for the ride . Just one thing -- you will be sitting still in it for a long long time. Make sure youre diaper has soft enough leg gathers and I'd recommend using some cream or something. I've had a few times where the leg gathers were held tight for hours from sitting and it started to burn eventually.
Brings back memories: my most memorable diaper change came in a moving bus! I got tossed aound pretty good in that little bathroom! It was actually kind of fun, even at the moment. Like an amusement park ride. Sorta.
If you can use your diaper while sitting in your seat on the bus, go diapered. Then you won't have to worry about using the bathroom on the bus (except for changes maybe). If you can't wet sitting on a moving bus, then there's no point in wearing that diaper. And please don't go #2 in your diaper on the bus, but that should be obvious anyway.
Have a safe trip!