I rarely ever have back problems on the bicycle, and I haven't got the strongest back.
1. Make sure your bicycle fits ... way back when, I was riding one that was a bit too big for me, and one side of my back used to cramp up. Well, I got a bicycle that fit, and no more back pain.
2. Ride all year round. I ease up for 2-4 weeks in the winter, but still remain active during those weeks. By this time of year I'm seriously ramping up my mileage again. Way back when, I used to be a spring, summer, fall rider, and would take at least 4 months off each winter. Each spring it was like starting from scratch again ... Ouch! It's so much easier if you keep going all year long.
3. You are a student ... therefore you carry a heavy backpack, right? Well ... walk lots with that backpack. I'm a student too, with a heavy backpack, and I walk 15-20 kms a week. Aside from discovering a whole new set of muscles, and building up my bones, I also noticed that my abs were tightening up because in order to walk comfortably with a heavy backpack, you've got to suck in those abs for additional support.