So first off, contact a CPA, don't depend on a jackwagon on the internet
for tax advice!
Having said that, this jackwagon will tell you that income is income under the U.S. tax code. There is no separate rate for "bonus" income vs "regular" income. Your marginal tax rate is based on whatever tax bracket you fall into, it's that simple.
Payroll withholding companies are required to withhold the appropriate amount for you so that if you're an average person you won't get hit by an extra big tax bill or refund. This means they are basically taking your anticipated total salary and withhold based on the blended rate you'll see if that's all you earn during the year. Since the tax rate is graduated by income, this blended rate is lower than your marginal rate, which is the rate you pay on each additional dollar you earn on top of what they initially calculated. As a result, when they do withholdings for a bonus, use the 22% rate, because the IRS tells them to because it better approximates your marginal rate. This may or may not be accurate depending on your other income. But in any event you're not paying more taxes because it was a bonus, you may be paying more taxes because the more you make the higher your tax rate on those last dollars earned. And at the end of the day, withholdings aren't taxes, they're an estimate, so your withholding rate isn't your tax rate.