Yes, I've taken the JR Dream Bus a number of times in my penurious student days. It's cheaper, but it's not particularly comfortable, and the trip is too short to allow a full night's sleep even if you can sleep well in what amounts to a Y seat -- the buses will dump you unceremoniously at your destination around 5 AM in the morning.

IMHO, since you have a Rail Pass, the 2.5-hour Shinkansen ride is a complete no-brainer. If you want to save the cost of a night's accommodation, look into love hotels or capsule hotels instead. (Alternatively, do what I did later on my student days and hitchhike...!)