It really ain't that bad, there are rough bits and fantastic bits.
Theres allways the risk of the odd random thing, but any city is like that.
I have never seena fight on a night out, the only time i have felt uncomfortable is 3am in the centre on a saturday night when the locals are out and there are people running up to you trying to scrounge money etc
I would not worry about it too much.
I won't say you will be safe, as i can't be sure. but stoke bishop and the uni (and what lies inbetween) is all the nice area of bristol.