I took a Greyhound once from the east coast to Colorado a long time ago with my best friend. I will never do it again unless I absolutely have to be somewhere and cannot afford to fly, drive or take a train.
That being said, just keep yourself entertained and you'll be fine. This was before buses had wifi, I didn't have a laptop or a kindle to read/watch anything. I would caution you to rely on wifi to download anything or stream anything. If the wifi even works, it's not that fast.
Anyway a word about the connections, if you are somewhere with a layover, make sure you are in line early. My friend and I actually had a silly connection (it was our first leg) from Baltimore to DC. We had a layover in DC for a few hours sometime after midnight. Anyway we get in line for the next leg to Pittsburgh and the bus fills up. They do not send a second bus because the number of people leftover was not enough to get another one, and the next bus wasn't until 7 am. Greyhound Bus stations are not known to be in the best areas of any city and after interacting with several sketchy characters at the DC bus station, we were lucky that we weren't that far from home and stayed at a friends until it was time for our bus.
We complained and Greyhound customer service is not the best, but they ended up giving us a food voucher for 5 bucks. Not exactly helpful but it was something.
We met some unsavory characters on the bus like rednecky pregnant moms who chain smoked and some just shady looking people, including one creepy guy who wouldn't leave my friend alone. BUT overall it wasn't too bad people wise, just maybe one or two weirdos per leg.
I've also taken Greyhound plenty of times between cities on the Eastern seaboard (Richmond, DC, Baltimore, Philly, New York) and the short trips are fine but I've had the same or worse experience with customer service at all of them. They do not have any patience. If you are late or holding things up they will not be kind to you. Not that most people would but Greyhound is used to dealing with a lot of people who are not "premium clientele" and I'm not saying that in a negative way against any one (obviously I've taken the bus plenty of times) but you get what you pay for. Note that if you have any experience with Bolt Bus (which is owned by Greyhound) it's several steps down from that experience. The buses are cleaner on Bolt Bus and the drivers seem much more upbeat and interested in making sure everyone has an enjoyable experience. Usually Bolt Bus drivers will do a little speech beforehand to make sure everyone keeps their volume low and goes over the rules. I have not experienced this with Greyhound drivers.
Definitely get out and stretch your legs whenever you have the opportunity. Make sure you have good headphones and comfortable clothes. Bring some baby wipes to freshen yourself up if you can't wash your face or things like that. Maybe bring a small towel to place on the seat- they might not be as clean as they look (which isn't that clean). Bring a plastic grocery bag for your trash.
I'm sorry I'm not giving you any positive advice probably but it's good to be aware of things so you're not shocked.