Mononucleosis is called glandular fever in some other countries. It's usually caused by the Epstein-Barr virus (EBV) and sometimes by cytomegalovirus (CMV). These viruses don't leave the body. Most older adolescents and adults carry one of these viruses without problem.
EBV is transmitted through saliva and the person you know may carry it in her saliva for up to 6 months after her symptoms have resolved. CMV can be sexually transmitted in semen. It's also transmitted through urine, saliva, blood, tears and breast milk.
Now whether or not you'll run into trouble, I cannot say. You may already have EBV in your blood. If so, good. You won't have any trouble. In all likelihood, you should be okay.