Littleadv is incorrect because receiving a 1099 means she will be taxed self-employment tax on top of federal income taxes. Your employer will automatically withhold 7.65% of payroll taxes as they pay you each paycheck and then they'll automatically pay the other half of your payroll tax (an additional 7.65%) to bring it to a total of 15.3%. In other words, because your wife is technically self employed, she will owe both sides of payroll tax which is 15.3% of $38k = $5,800 on TOP of your federal income tax (which is the only thing the W-4 is instructing them about what amount to withhold).
The huge advantage to a 1099, however, is that she's essentially self-employed which means ALL of the things she needs to run her business are deductible expenses. This includes her car, computer, home office, supplies, sometimes phone, gas, maintenance, travel expenses, sometimes entertainment, etc - which can easily bring her "income" down from $38k to lets say $23k, reducing both her federal income tax AND self-employment tax to apply to $15k less (saving lets say 50% of $15k = $7.5k with federal and self employment because your income is so high).
She is actually supposed to pay quarterly taxes to make up for all of this. The easy way to do this is each quarter plug YOUR total salary + bonus and the tax YOU have paid so far (check your paystubs) into TurboTax along with her income so far and all of her expenses. This will give you how much tax you can expect to have left to owe so far--this would be your first quarter. When you calculate your other quarters, do it the exact same way and just subtract what you've already paid so far that year from your total tax liability.