If you are a US citizen or green card holder, you owe US tax on all your world-wide income, no matter where you were living when it was paid. If you also pay tax in a foreign country on the same income, you can claim a deduction or credit on your US tax return to reduce the double-taxation.
Tax withholding on bonuses is controlled by a specific IRS formula that sometimes (but not always) overestimates the tax on the bonus. At the end of the year, you file one tax return that lists all your income and all your withholding, and calculates your total tax bill. If your withholding was more than your tax bill, you get the difference as a tax refund. There is no way to apply for a refund in the middle of the year, due to a bonus or any other reason.
