That usually happens to any vegetable which touches the ground. But if that isn't the case, I have no explanation... Maybe a plant virus in the soil? Or bacteria perhaps? To rule out this possibility, try planting some more, but in containers, (with no link to ground), and in another area of your house. That at least would tell us if the soil is to blame or not. Doubt if this is because of over watering. As bell peppers do fine in hydroponics. So I really have no real explanation... Could it be spider mites I wonder??? If this is bell specific and no other vegetables growing nearby are effected - Then I am confused further...
This is a classic case of Calcium deficiency. Remedies are, eggshells or lime or Epsom salts. Be careful to water not too much or too little. Do not give too much high nitrogen fertiliser. Mulch around the plants too. Cold weather at the end of the season also stops plants being able to absorb nutrients efficiently. If you have lots of dandelions, this indicates low calcium levels. If your soil is alkaline, lime is out of the question and gypsum is preferable.
Very similar to blossom end rot in tomatoes ! Use about two tablespoons of epsom salts about 6 inches away from the main stem,,one on each side and water it in ! You can also do a foliar spray,, with 1 tbsp epsom salts to a quart of water! Spray leaves early morning before it gets hot ! You need to add epsom salts at planting to prevent this ! Like Odif said a little lime sprinked on the top of the soil snd watered in would help also !
Yes I understand that amongst other magical properties, epsom salts assists in making existing calcium more available to a plant.