There are 2 ways to get to Hormoz island from Bandar Abbas. By far the easiest will be by open speedboat (2,5$, 40 minutes) from Shahid Haqani port (map) to the quay in Hormoz. Boats leave often early in the morning but far less often in the afternoon. Time your return before 3pm to be sure of a ride back to Bandar Abbas.
The other way is to hire a dhow. The sailing time will be much longer and you will need to make arrangements in advance. There is no scheduled boat from Qeshm island to Hormoz.