At Bill Free Homes we try to give you as many ideas as we can to avoid bringing a car.
In some houses further from the city centre we bundle the cost of an Arriva Student Bus pass in with the rent . The pass allows unrestricted use of Arriva buses the Durham City zone on the route map shown here 
If you would like to know more you can do so here 
We are happy to assist if you need more information.
Durham Timetables can be found here
Do  remember if you are going to Newcastle  the  trains  do  not run that  late and  there are  night buses  to  get  you  home.
Check out the  N21 timetable here.
Please see the  University Information on the Free Buses  it  provides which are predominately  the X1/X2 and  the U1 to  Ushaw College