Bell assumptions:
1. It should agree with the predictions of Quantum Mechanics (so as to agree with established experiments).
2. It should adhere to the principles of relativity (causes cannot propagate faster than the speed of light) - this is called Locality (sometimes Bell Locality). Specifically, a measurement setting for one member of an entangled particle pair should not affect the results of a measurement on the other member of the pair located at a distance. Otherwise, you would have so-called "spooky action at a distance".
3. There should be simultaneous existence of the elements of reality described above (A, B and C, for example). This is often called "Hidden Variables" or sometimes "Realism".
A person who believes in assumptions 2. and 3. above is called a Local Realist. These two assumptions are very reasonable, and there were a lot of physicists who believed them before Bell. Why not? You simply accepted the predictions of QM and assumed that 2. and 3. were true too. But... Bell showed that the three assumptions above are actually incompatible when combined. Therefore, at least one must be wrong. Bell derived a specific testable prediction related to this called Bell's Inequality. If Bell's Inequality is correct, then the first assumption is wrong. This was the line in the sand for the Local Realist.
I find all 3 assumptions true:
1) Predictions are right, interpretations are wrong.
2) There is no mystical interaction between particles
3) Yes, hidden variables, defined properties before measurement