We had the same worry as well. We spoke with the gentleman who came to our room to collect our bags. He said they go into a holding area "with all the rest of them."
This gave us some comfort. Our bags aren't the only ones. There are lots. They have a system. Sometimes you just have to trust the system.
That said... my DH's bag and our garment bag arrived relatively soon after we boarded ship. We met our room attendant and asked about my bag. He said there we many more bags coming and assured us not to worry. I had accidentally left some medication in my bag so we were checking for it frequently. No bag. Enjoy the buffet. No bag. 20 minutes until sailing... no bag. Yeah, I was worried. However, there was just nothing to do about it at that point so off to the Sail Away party we went.
When we came by the room about an hour after sailing -

LOOK! THERE! In the hallway!

MY BAG!
The system works. Tag your bags appropriately. Let them know your ship. (Tipping nicely can't hurt.) And enjoy the hassle-free nature of it all - it works - and you're on vacation!
- Dreams