Most people don't really need to wear a weightlifting belt while performing a bench press, especially if your strength training routines are mostly health- or recreation-focused.
That said, bench press requires core stabilization, and a belt can help remind you to keep your core engaged.
Additionally, if you're trying to max out on bench press, or lift more than you typically would, the extra support of the belt may help you lift more than you would without a belt.