MySymbolScript is specific to a given symbol, so there will be one instance (copy) of it for each symbol. There will only be one instance of MySystem no matter how many symbols you are using. So the reason the bar data isn't directly accessible in MySystem is because there's no way to know which symbol you are referring to.
You can add a Shutdown method to your MySymbolScript class, and then you can have your MySystem's Shutdown method call the symbol script shutdown method for each symbol like this:
public override void Shutdown()
foreach (MySymbolScript ss in SymbolScripts)