Question

Which of these plays the largest role in interpreting the bill of rights? congress the executive branch state legislatures the supreme court?

Answer 1

The bill of Rights is part of the US constitution, (the first 10 Amendments), so they will be interpreted by the same institution as the one that interprets the constitution generally. 

This would be the Supreme Court of the United States - specifically, the Supreme court checks whether the laws passed by the congress are compatible with the constitution