If you are a NY state resident filing form IT-201 then only enter the bonus amount in Column A "Total Amount." If you are a NY nonresident or part-year resident filing form IT-203 then enter the the total in Column A and the portion that relates to NY source income in Column B.
If you use the step-by-step interview in TurboTax as @rjs mentions the amounts will populate the correct columns and forms for you.
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