I am guessing that bus will be the best way to get to Yixing. From a quick web search, looks like it's a ~ 3H bus ride.
See, e.g., http://www.transportinchina.com/bus/sha ... timetable/
Train will be ~ 15-20 hours to Xi'an, so you might consider flying, but train (hard sleeper) might also be an entertaining way to go, depending on how much time you have (at least one direction). Unfortunately, reservations can be a little tricky to deal with in terms of Chinese trains, but there are good translations of timetables if you search online.