Hi, first of all could I ask why November 20th is the specific date you want to lose weight by? Is there a special event? Also, do you want to lose weight just for this date, or do you want to lose it and keep it off and keep being fit and healthy (i.e. will you keep going to the gym after November 20? will it still be twice a week?)
There was some good advice above - you really need to look at your eating habits if you are going to lose weight. Roughly, you need to cut down or cut out takeaway foods and cut out sugary sweets/soft drink. Try to eat 5 serves of vegies and 2 fruits every day. Your calorie needs will be higher than an adult of your size because you are still growing, therefore I'd recommend speaking to your GP or a dietician (some gyms have them, does yours?) about how to diet safely while you are still growing. It is important you still get the calories you require to continue growing and maturing!
In regards to the gym, it's great that you are going twice a week and it sounds like you are working hard at the bike. Make sure you do some weights too, this will help you to build muscle, which in turn burns more fat. Even if you can't make it to the gym on the other days, you will lose weight faster if you do some sort of exercise - can you go for a walk/run, play footy, go swimming, take the stairs everywhere you go, etc? That will help you best in the long run.
Good luck! I stress again - it's best if you see a professional such as a doctor or a nutritionist to examine your diet - for a growing teenager, your needs will be different to an adult so Internet sites and advice you get here may not be accurate or relevant to you.