How long should steri strips stay on after a bilateral breast reduction? Should I be retaping? Had surgery June 13th.

You may have misunderstood your surgeon.  He probably said the Steri-Strips would gradually fall off as you shower.  There would have been no reason to put them on if they were going to fall off the same night.  Steri-Strips will often stay in place for 1 to 2 weeks.  Their job is to continue to support the incisions. 
As far as whether you should replace them, I would be in contact with your surgeon's office as to the best care after they come off.  Some surgeons recommend various types of topical treatment for the best scars.  Ask your surgeon's office what they recommend.

Each doctor has his/her own protocol following surgery.  I would recommend that you contact your plastic surgeon to see how he would like you to proceed.  Personally, I don't usually leave steri-strips in place for more than a week.

I prefer that my patients use tape on their incisions for about 6 weeks or so. This can be stern-strips or paper tape.  Best to review with your doctor.

If the stapes are still holding, I would leave them alone. Once gone, you can probably start scar products on your incisions. However, it would be best to call your surgeon and ask these questions. Every surgeon has his/her preference about tapes and wound care.