A number of banks offer a Student Railcard when you open a student account, which gets you a third off all train journeys, which is obviously good if you use the train a lot! You can buy them too, but I can't remember how much they are off the top of my head.
I don't think students get reduced fares on buses - well, they don't around here anyway. Depending on how many times you use public transport, it can be worth getting a pass. A pass for bus and metro for a month in Newcastle, for example, is about £30, so if you're spending £3/4/5 a day on transport it can be well worth getting.
Railcard is £20, or free with some bank accounts.
it depens on where you are planning to study. in london a railcard costs £5.70 per day and i think the discount available is 1/3 off