Regular chlorine bleach will work in well water, but since the volume in the well usually isn't known, it's usually better to treat the water in a container of known size so the dosages are correct.
When we had a well, I used plain old 'Clorox' bleach.
None of the 'Smell Good' or 'Color' they like to put in things now.
Later we used the water treatment chemical power like they use in swimming pools and water treatment plants.
Cheaper and didn't take as much work to get the smell out.
To take the chlorine smell/taste out, simply aerate the water.
Chlorine is volatile and will evaporate/evacuate the water simply pouring it back and forth from one container to another.
There are several chemical filters on the market that will take chlorine out of water also, they are cheap, easy to install in a pressurized water system, and they are nearly 100% effective.
The water flows into, AND OUT OF wells all the time...
A well is nothing more than a deep spot on an underground stream, and if you pour the bleach in the well, it will be migrated out almost immediately and replaced with 'Raw' water.
It's much easier and more convent (not to mention using a bunch less 'Bleach' or whatever!) to have a large reserve tank, and when the tank is refilled from the well, add the bleach.
Since you know exactly were the pump comes on and when the pump goes off, you know how much water (within a few gallons) has been replaced in the tank, and most places with a 'Bad Well' have automatic cycling treatment tanks anyway...
When the tank gets full, it looks like a toilet tank float that administers a metered amount of disinfectant into the water... every time the tank is refilled...
We have two wells - One is low (or is to high) PH that was corroding the copper pipes. When we built the in law house, we used plastic plumbing pipe and now use that well on that house.
We dug a new well which has great water properties but get a little iron algae that we treat with plain old bleach every 3-6 months. As someone else said, don't use anything but plain bleach and do not use chlorine.
We have both wells tied together so if one run's dry, both houses can be served by either.
A while back (29 yrs) the check valve at the bottom of our well had to be replaced. When finished 2 gal of chlorine were dumped down the well to take care of "whatever". After a couple of days, the taste wasn't detectable. It has been good tasting ever since.
A friend had a well that was polluted by a bad septic system. I do not know where, but he bought a chlorine injector that held and put a set amount of bleach into his pressure tank every so often. The well is still in use today, and all he does is send in a sample to a lab every 6 months. With the bleach, the water comes back fine.
When I lived in Maine, I had to clean our well yearly. Basically I created a strong chlorine solution, poured it in the well, waited, then purged the well. I am being vague because the details depend on your well.
Check with the state board of water quality, state health agency or similar groups to find details calculated for your well.
This is a very common practice in rural areas, especially areas which have a certain bacteria which smells like sulpher (how is it spelled??). Don't guess, get the facts.