How much more calories to consume during days with high calorie burn...?

As of typing this, my current calories burned is at 538. I'm planning to do 90 minutes on the stationary bike in light to moderate effort (and I've probably done that by the time anyone replies to this post) which would result in 1174-1346 cal. Since I'm stuck with cooking and cleaning in the household, I'd surely be adding some more to that when the evening comes.

Now, my question is if I burn that many calories for the day, how much more calories should I consume? I usually keep my calorie intake between 1200-1300 cal since I'm aiming to lose at least 40 lbs by my birthday on October 22 so I want to know how much more am I supposed to eat to balance my intake with what I burn. Would 1500 cal suffice or should I consume more? If so, how much more?

If you burn 1200ish, you MUST eat AT LEAST 2000. Think about it - if you eat 1500 and burn 1200, that leaves you with only 300 to function off of. Yeah, well under starvation.

If I were you I'd even go as much as 2500...

I'm not sure how you are estimating the amount of calories you are burning, but if you're going by the "counter" on the exercise machine, just keep in mind that they usually double the amount you actually burn (if you're already in decent shape). I'm in pretty good shape, so I might burn a maximum of 400 calories in an hour of moderate to heavy exercise-- maybe 200 in light to moderate... Just something to keep in mind if you're "making up" the calories on the other end. Exercise is great, but is not the most efficient weight loss tool if intake is not kept in check. That said, I'd raise your intake to at least 1600 on days you work out for an hour at mod-hi intensity or 90 min of low-mod intensity.

Are you using the site tools to calculate your total daily calorie burn including exercise.  Once you do this you can see how much you need to eat to to lose weight at a safe rate.

You would have to lose 2 lbs a week to reach your goal which isn't a realistic expectation.  You may be able to lose at that rate in the beginning but you will need to adjust your eating to remain at a healthy level as you get closer to your goal weight.

Yes, I am using the site tools to calculate my daily burn. And yes, I know I'll have to change what I do as I progress but I want to see what I can achieve in a month's time since I've never counted calories nor have I ever monitored what I do and eat each day. And I don't want to under-eat and over-exercise and ruin what I'm doing.

My goal may be unrealistic but if I'm gonna dream, might as well dream big and try the best I can. If I reach it, good for me. If I don't, then I'm well on the way to doing it. No harm done either way.

So add your exercise to the log to come up with a total burn for the day and then eat 1000 calories less than that.  As long as you are over 25, female, and that number isn't below 1200 you should be okay for a while.

Actually there is the potential to do some harm.  If you habitually under-eat two things are likely to happen.  First, there is only so much fat your body can metabolize in a week.  If your deficit is too large you will end up losing extra muscle which is something you don't want to do.  Additionally, you could end up stalling your metabolism from under eating which can make it even harder to lose weight and easier to gain weight back.

So it is important to calculate your numbers correctly so you don't do yourself harm.  It may sound like a good goal but 2 lbs/ week sustained is actually a very aggressive goal.  I don't know anything about you so maybe it is a possibility for someone your size.  But if not, my opinion is that you are more likely to stick with your plan if you have realistic goals.  When goals are unachievable people tend to give up trying.