The reason that situps are bad for your back is that it produces a high amount of pressure on the discs when the spine is in flexion. When you are just laying in bed there is only 25 lbs. of pressure. When you sit up, the pressure shoots up to 180-210 lbs. The flexion of the spine also pushes the disc posteriorly ( to the back). So if you do this enough it will eventually wear down the disc and cause a disc bulge and/or herniation. We unwittingly do a sit up every single day every time we get up from bed.
1) Lay on your side facing the edge of the bed
2) Drop the legs over the side of the bed
3) Push your body up with your elbows and hands to sit up
No flexion involved!