Check the bus route ahead of time so you will know how long the trip will take, as well as knowing where the stops will be. Wherever you bought the tickets from should have access to this information, whether it is online or at a bus depot.
Pack a small bag with items to take on the bus with you. Bring snacks, drinks and activities to pass the time.
Dress in layers or bring a blanket with you. The temperature on public transportation is always unpredictable and at least you will have a way to stay warm if it is chilly.
If you are traveling a long distance, chances are there will be stops every two to three hours. It's a good idea to get out and stretch at the stops even if you do not feel like it. It helps make the overall trip more enjoyable.
Gather your things before reaching your destination. You will have more time and less chance of missing something in the confusion of people standing up and getting off the bus.