Mazal tov on your upcoming wedding.
Doing a bedikah is a safe procedure. Prepared bedikah cloths that you can purchase are clean and never previously used in any way, but not in fact sterilized. However, as the vaginal canal is open to the outside environment, it is not a sterile environment. Therefore, items placed inside, such a bedikah cloths or tampons, must be clean but not sterile. From a health point of view, it is also important to note that items such as tampons, should not be left in the vaginal canal over 24 hours. While there is no halachic situation where this would be necessary, women have been known to forget and leave in a bedikah cloth as a moch dachuk longer than needed. This should be avoided.