A military bonus is taxable just like your regular military pay, unless it falls under the combat zone exclusion. The combat zone exclusion is detailed in this federal statute:
https://www.law.cornell.edu/cfr/text/26/1.112-1#:~:text=CFR-,%C2%A7%201.112%2D1%20Combat%20zone%20co....
In short, money earned while you are serving in a combat zone is tax-free. This can include your reenlistment bonus, provided you signed the reenlistment paperwork while you were in the tax-exempt combat zone. This also covers your annual installment bonuses, even if they are later received when you are no longer serving in the tax-exempt combat zone.
However, if you signed the paperwork outside the combat zone, it is not tax-exempt, even if you receive the bonus or annual installment while you are in the combat zone.
**Answers are correct to the best of my ability but do not constitute tax or legal advice.
