It is my understanding that calories expended need to exceed calories taken in by about 3600 calories to lose one pound.
Healthy weight loss is supposed to be 1 to 2 pounds per week (as stated by several weight loss sources).
Assuming before cycling your diet maintained your weight, then I would say to decrease your intake by about 500 per day, and increase your activity by about 500 calories per day, and and you will lose 2 pounds per week (or some other variation that leads to a 1000 calorie deficit per day).
Do your exercise at a reasonable pace (as stated elsewhere, a relatively slow pace seems to work better).
Drink lots of water, and very little of the things that will make you fat (including sugar and alcohol).
Do strength exercise as well, to increase muscle. This is good for two reasons. 1) it makes riding more fun, 2) muscle is active tissue and burns calories as opposed to fat which is passive tissue and does not.
Don't be disappointed if your weight doesn't come off on some weeks, especially if you did the work and feel healthy, because at times you will be gaining muscle, which offsets the loss of fat on the scale. This however should not be used to excuse too many weeks in a row.
I have lost over 100 pounds, but not much lately, so take all of this with a grain of salt... When I get to my goal weight, I will be able to say accurately, "I am half the man I used to be!"