I would definately get the well tested. I can't believe you were told to bleach the well before testing!! The $20 test I had done on our well includes a test for bacteria (Coliform). If you bleach it, you won't get an accurate test. I think our test included chlorides, they would be way high if you bleach. I wouldn't EVER drink from a well that hadn't been tested. With all the polution these days, you can't be too careful. Our well is too high in nitrates, had lots of bacteria. When they put in rural water in this area, the people that owned this place didn't hook up. I can just hear the old farmer saying "there aint nothing wrong with this water, it tastes just fine". Maybe that was true (sometimes) in the past but not today. His son who grew up here died of bladder cancer. His friend who spent a lot of time here also got bladder cancer.
I can't believe that the county agent said that you don't need to bleach unless it tastes or smells bad. What a joke. Sulfides can cause a bad smell and have nothing to do with bacteria. You can have high bacteria and no bad smell.
I also can't believe that someone said that bleach was useless to treat a well. How much to put in depends on how much water is in the bottom of the well, not how deep it is. I put about a pint in mine and it smells like a swimming pool for a few days. I have a spigot right next to the well. I put a hose on it and recirculate the water into the well and rinse the well bore. Then run it thru all the pipes and let it sit for a day. Then run the chlorine out if you want. Be careful with the laundry, even after the smell is gone, it can bleach your clothes
My in-laws live in Salina KS. They used a well for many years. When I met them in the 70's I thought the water had a funny taste and smell. The older kids are pretty healthy, but the younger ones have had all sorts of health problems. Over the years, the water got worse. The well eventually wasn't usable. In the late 90's, it came to light that there was pollution coming from the old air base 2 miles away. Some cleaning solvent was just dumped on the ground in the 40's and 50's. Now there is a plume of spreading pollution heading for the town. It won't be too many more years before it spreads to the town's wells.
We live in a scary world.