There are too many variables.

Some things that you can do, will need to do, etc:
1. Riding requires muscle adaptation. Your fit/position will change over time. It'll start out with the bars higher and closer, and as you get more fit you'll find that you can move them down and further out.
2. If you're not moving around a bit it'll be uncomfortable. Stand, sit, use the tops, the drops. Don't lock yourself in one position. Stretch your back even.
3. Core strength - do abdominal stuff while in front of the TV. 50 crunches at a time, sit ups, whatever, virtually anything is better than nothing.
4. Pre-existing condition?

Things you may need to do with your bike:
1. Bars too low or too far away or both
2. Although counterintuitive, bars may be too high or too close. Sitting sort of upright can really stress your back. It's like sort of leaning over the kitchen sink to wash dishes - I have to stand straight up else my back starts to seize in just a few minutes. On the bike I have a longer, lower position, appropriate to my body dimensions, and on my bike I have no back issues even though I have some actual back issues.