The 360 (or really, anything De Courcey) is the cheapest way to get anywhere (take your student card, though: only 80p with it!). For quicker (but more expensive) options, you could get the 11/12 (or variation thereon) to Hearsall Common or the train station, then the 1, 9 or 9A to university hospital; or your preferred bus to Pool Meadow then the 4, 16 or 16A to University hospital.