In the U.S., you typically need to apply separately to graduate school; it's not simply a matter of "staying longer." You would take the GRE and/or GMAT during/after your junior year, and then apply to business or other graduate schools no earlier than your senior year in college.
The more prestigious MBA programs (Stanford, Wharton, Harvard, etc.), however, don't accept recent graduates with business degrees; they prefer applicants with three-to-five years of real work experience.
So, unless you apply for (and are accepted to) a dual degree BS/MBA or BS/MS program, it's not a decision that you need to make now. And even if you do (and are), you can always decide to finish after your BS is complete.