Just reenlisted for a bonus.. taxes?

As the title suggests, i just reenlisted and will be receiving my bonus within the next month. Can someone who previously received a bonus explain to me the tax implications?

I understand that bonuses are viewed as “supplemental income” by the IRS and taxed at a flat 22% on balances under $1mil. Is that just withholdings and, assuming i overpaid my tax liability for the year, i should expect to receive about half of the upfront taxed amount as a tax refund. Or, is it just taxed at that 22% overall and i should not expect a higher than usual return?