1000 calories a day is starving. I've been trying to lose the 30 pounds I gained on lithium, eating only 1200 calories a day, and the pounds are just not coming off. My daughter, who has OCD and does meticulous research, successfully lost 40 pounds last year by exercising 1/2 hour a day on her treadmill and eating 1500 calories a day. She said that 1200 calories a day is starvation mode. She told me that your body goes into starvation caveman mode and holds onto every calorie as if there was no more food ever. Try eating a little more than you have been.
Riding a bike is great exercise, but on 1000 calories a day, you may have been overdoing the exercise.
I've also been doing some research for a diabetic friend and I found that a diet with a low glycemic index will not only help stabilize your blood sugar but will help you lose weight at the same time. Instead of quick oats, eat steel cut (long cooking) oatmeal. Instead of a banana, eat an apple, and so on. Every little bit helps. I lost 3 pounds this month on my daughter's plan.
Another recommendation from the Canadian Diabetes Association is to stagger your meals throughout the day. Instead of two meals, eat the same number of calories in 3 meals and two snacks. When you eat 5 times a day, you don't get as hungry and you don't get as many food cravings.