My wonderful hubby bought me a nice hybird bike, it can do a little road and a little mountain biking but it's not great at either. But it's been perfect for the terrain around my house, a mix of paved road and rocky dirt roads.
Last two days I have set my alarm early and have gotten out before my kiddo & hubby woke up and did 10-13 miles.

According to various calculators it says I am burning about 650 calories an hour at 13mph cycling for my weight.

I am currently eating between 1300-1500 calories a day (it varies but I eat 3 meals a day, under 500 calories each)

I plan on cycling for 1 hour everyday (so about 650 cals burned).

So obviously the last 2 days I have been hungry because I don't usually exercise.

Any advice on how much I should be eating to lose 2lbs a week?

Certainly don't eat back the calories you've burned... to start I'd say add 200 calories and work from there... Congrats on getting up and out early... I'm just back from a 10k/6.2m ride, 30 mins, and it's only 6:20am ... I almost didn't go because I got only 4 hours of sleep last night, toss and turn, toss and turn... but I did get up and am happy I did...

It actually depends on the rate that you're losing. If you're losing 1.5 - 2 lb a week, with 1300-1500 calories, then I would "eat back" the calories you're burning on the bike.

The only thing is, you don't really know how much you're burning, so I would see how it goes if you do start eating back those calories. You can start eating back the 600 and see if that stalls your weight loss. If it does, then eat 500 or 400 and see how that works.

Cycling is a lot of exercise and what you don't want to happen is to deprive your body too much of the fuel it needs -- and yes, it uses it to exercise as much as lay around the house or go to work. And the last thing you need is to restrict yourself so much that on the weekend (or some random night) you gorge on food because you've been depriving yourself!

Just remember to eat healthy -- 600 calories is not a license to eat a sundae, it just means you can eat a slight larger lunch.

I go out for quite long rides and I am struggling with the same. I take about 400 extra calories per hour and a half with me and see how it goes on the road. It's mostly fast-carbs that I eat on my bike. I don't eat extra once I am home. I really use it as fuel when I am on the go. It depends on what you want out of it too. I notice you can't really improve on the cycling if you cut calories and you can't not cut calories and drop the weight. LOL.

So right now I focus on doing decent on the bike, learning the small stuff and technique and once I am at goalweight I will focus on speed and stuff that costs more energy.

Just really make sure you drink on the bike and always have something with you to eat because if the hunger hits you all at once, omg that sucks.