You will need to file a Georgia nonresident return.  This is the only way that you can get the tax refund on the amount you are paying to Georgia.  However, it is possible that the amount actually is taxable to Georgia if the bonus was earned off of your work in Georgia instead of North Carolina.  You may want to check with your company on this.  Either way, you still file a Georgia nonresident return.  And, if the amount is not taxable in Georgia, you will allocate the income to Georgia as zero so that the taxes can be returned to you.

If, however, the amount actually is taxable to Georgia, North Carolina will give you a credit for the tax you are paying to Georgia on that income.  Your final result, then, should be about the same.  To assist TurboTax to calculate your credit correctly, you should prepare the nonresident return first.  The following FAQ has more information on this:  https://ttlc.intuit.com/replies/3302052