David,
You are, of course, correct. The best way to store a choose-many would be just to record each answer in a table like: SurveyID, QuestionId, AnswerID [AnswerText]. Allowing each SurveyID, QuestionID to have multiple answers. You then need to do some checking on the choose-ones to make sure that you don't accept multiple responses for those questions.
I found that the bitmask method made it easier to create the data entry form at the cost of more complicated reporting.
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JimFive