Depending on where you are coming from, you will find a couple of bus companies that will take you Mohegan Sun. By bus from NYC to Mohegan Sun will take around 4 hours and most people will purchase a round trip ticket.
Most buses from NYC will leave early evening (between 6-8 pm) arriving late night and then depart Mohegan Sun early morning (between 4-6 am) at a price of usually $18-22.
While doing some research for a friend, I found this bus company, Gotobus.com. Check out their website for more information.
We always drive to Mohegan Sun, it is the easiest and most convenient way for us to get there, which usually will take us anywhere from 2-3 hours, depending on the traffic and time of day.
We hop on 95 North to Exit 76 (395 Noth) to exit 79A (2A) to Mohegan Sun Boulevard which is then about a few minutes to the casino.
When we stayed at the Best Western they had a complimentary limo service to Mohegan Sun. This was a fast and free way to get back and forth from the Casino to the Hotel.
Driving is our preferred way to get to Mohegan Sun. We are barely 5 minutes from the Connecticut border so jumping on the highway is a snap.