Hi there, @puniversity.
Let me enlighten you about the calculation of payroll taxes in QuickBooks.
Yes. Payroll taxes will automatically calculate based on the gross pay of the paycheck. Thus, the bonus paycheck won't deduct any employee deductions before it calculates the payroll taxes.
In case you want to learn more about retirement plan deductions/contributions, feel free to read this article: Retirement Plan Deductions/Contributions.
You might also want to check out this article to know how to prepare for payroll tax set up.
Please know that you can always get back to this post if you have additional questions. We're always here to help.