When we left Beijing on the bullet train for Shanghai we did have our tickets purchased already.
I noticed, however, that it was very easy to buy tickets at the station using a machine. There was an English option, and it was a simple touch screen method, showing all trains and which ones had seats available. I am guessing that it is exactly the same process in Shanghai.
Our train leaving 40 minutes later was sold out except for Business class (a lot more money), but the train leaving only 5 minutes later had seats available.
To use that method of purchase, you need to have cash available to insert into the machine, the fare is 555 yuan.