How can I reduce back pain on a shared bike with poor shock absorbers I ride a bicycle to work every day for several months now.
I use a bicycle sharing system that my city offers, and it's very convenient: I don't have to worry about locking the bike or maintenance, I can use the bike only one way etc.

However, recently I've started having back pains, and I think it has to do with the fact that the bikes in the sharing system don't have good shock absorbers, and I can feel every bump in the road giving me a strong jolt.

Is there a way I can reduce the damage to my back while still using the bike sharing system?
I seriously doubt that it's due to the lack of shocks, unless you have some really bad roads there -- many people ride bikes great distances with no shocks, skinny, stiff tires, and no real springs in the seat.  

More likely your problem is with your posture -- seat too low, handlebar too low, handlebar too close or too far away, and/or pedals at the wrong angle to the seat.  

Presumably you can adjust the seat height, so the first thing to try is to move it a bit higher.  When the seat is at the proper height your knees should be nearly straight at the bottom of your stroke.

Next, see if you can adjust the seat forward/backwards.  Being too far either direction can cause back problems, so try several positions.

You probably can't adjust handlebar height, but if you can, try raising it.