Hi Sandra,
I'm sorry to hear about your back. You do need to exercise caution so that you don't further aggrevate it and cause an injury. A stationary bike should be fine, although some people with back problems prefer the recumbent bikes because of the positoning. They tend to place less stress on the lower back. If you have access to a pool, swimming is excellent. Being in the water is very low-impact, provides a bit of resistance, so that you can help to safely strengthen the muscles, while getting a good cardio workout in. Yoga and pilates may also be for you. If walking doesn't bother you, this is also good exercise. You want to aim for at least three days per week of cardio exercise, approximately 30 minutes each time.
You may want to check with your doctor or a phyical therapist to see what he/she recommends as far as safety for you. There are many great stretching exercises that can help. For burning an optimal amount of calories and fat, strength training is also important. A good physical therapist can help guide you through the exercises you can do (and amount of weight, if any to use) that will benefit you.
The good news is, you can still get in a good workout. Keep up the diet as well, and you should see some great results.
Good Luck,
Paul