Hello TravelisFun,
I bought the same kind of ticket and did both climbs back to back about two weeks ago. The lines is long for the Dome climb and they DO check your entrance time closely. If someone is in front of you that has a later time, they`ll ask them to move out of the way. There is only one entrance for the Dome climb and that is to that left of the entrance with the Baptistry at your back. For Giottos bell tower, I just went to the entrance, showed ticket, and got my pack inspected, and up I went. I hope I answered your question. Have fun!