Is there a way to get money back on a reenlistment bonus that they took 25% taxes out of

sure. when you file a return for that year, request any excess be refunded. There is no other way.

I meant to ask is what are the steps to do that? This is my first bonus 

The reenlistment bonus should be included along with your wages on your W-2 in box 1 and the federal income taxes withheld for both you wages and the bonus should be in box 2 .

The TurboTax program will enter your your federal taxes withheld on your Form 1040 on Line 25a as a tax payment.

@mercedes1702 Your W-2 is going to show all of your income in box 1 and all the federal tax withheld in box 2.  The software will use those amounts to calculate how much your refund will be.   You do not have to do anything special----just enter all of the information from all of the boxes on your W-2 and let the software handle the calculations.