Depends if you are nursing or not, and whether or not you are planning to alter your eating habits at the same time. If you are nursing, it is generally considered not a great idea to lose more than a pound a week, so 10 weeks would be a reasonable timeframe. If you are not nursing, then you can safely lose about 2.5 lbs per week, but if you just add 1/2 hour of biking per day and don't alter your food intake at all, you will lose less than that. Depending on how hard you ride, you could burn around 150-350 calories in half an hour, and as one pound = 3500 calories, it would take a minimum of 10 days to lose a pound. If you alter your eating habits at the same time and run a daily calorie deficit of a couple hundred calories you could lose up to that 2.5 lbs per week, in which case 4 weeks is a reasonable goal (also, you tend to lose a couple pounds of water weight right off the bat if you start "dieting").
1-2 pounds a week is what most people say is healthy and best for long term results. I think Eat to Live is amazing though, and you can lose it much faster and it stays off. On Eat to Live I pretty easily lost 5 pounds the first week, and maybe three the second and two the third, so three weeks for 10 pounds that stayed off even after I totally fell off the diet wagon and so need to get back on.