The fact is, bleaching carpet is not like getting a stain on carpet that can come off with the right stain remover, it is a process that actually removes the color from the carpet. So, your options are basically, cover it up, cut out the bleached area and replace it with new carpet, or try to dye it back to the original color. However, each of these have inherent risks. For example, if you do a poor job replacing the bleached part your carpet could look really awful. If you try to dye it and do a poor job, it could actually make it look worse.
So, instead, do the following:
Make sure you have home owner's insurance to cover these mishaps. It stinks when you have to pay out your deductible, which is usually $500 to $1000, but the fact is, replacing carpet in a room usually costs more than this, so it is worth it to make the claim if you have a bad bleached area, or can't seem to fix it or cover it up. So, check with your home owner's policy to see if you are covered for these kinds of problems, and if you aren't, it might be a good idea to add this coverage, as mistakes of that kind can happen to anyone.

Keep cleaning supplies locked up tight where kids can't get to them. Most of the time carpet gets bleached because a child grabs a bottle of toilet bowl cleaner, and drips it all over the floor before you realize it. So, eliminate much of what causes the bleach spots to happen in the first place by keeping cleaning supplies well out of the reach of children and locked up tight so that they do not get into them. If you are cleaning your bathroom, for example, do not leave your cleaning supplies unattended.

Get rid of your cleaning supplies and invest in some vinegar and baking soda, it can clean almost anything. Instead of using harsh chemical cleaners that could be risky and bleach out your carpet, get a bottle of white vinegar and a box of baking soda, as this can clean almost anything. They are natural cleaners that are not toxic. They are green, and they are going to be much safer for the home with small children. They can be used to clean stains off counters, toilets, stoves, etc. they are the perfect multi-purpose cleaner.
If you bleach your carpet, know that your only sure option is replacement.