The bonus is considered "supplemental wages." There are special rules for withholding on supplemental wages. Those rules are in a different IRS publication, Publication 15, (Circular E), Employer's Tax Guide, Chapter 7. Basically the employer has the option of withholding a flat 22% on the bonus instead of treating it as if you made that much every pay period. Would that solve your problem? You are going to have to pay tax on the bonus, so you would want to have some tax withheld from it. It's the employer's choice to use that method, not your choice, so talk to the payroll department. Maybe that's what they're going to do.
If you've already started the job, it might be too late to change your W-4 for the first paycheck, and it might be too late to get them to use the 22% method if they were not already planning to do that.
