Debbie,
You can't judge by us, we were the first Carnival cruise to leave that port and there were no other cruises that day, so the parking lot was not full. You do pull up and leave your tagged lugged with a porter (you can also drop your companion off at the same time) and then go park. The parking lot is right there, my husband dropped all of us off and then went to park the truck...he was so close I walked over to meet him. We parked in the main parking lot, I do not know where the extra parking lot is.
I will tell you when we got back, the parking lot was packed, really packed...cars were parked where they shouldn't have been. Because everyone was pulling up to the spots where you pick up your luggage from the porter, it blocked the main drag out. It takes a little bit of patience.
As long as your luggage had the tags Carnival gave you, you can just drop it off.
We drove down from the Dallas area, and stayed overnight at the Crowne Plaza in West Houston. Then drove from there the day of the cruise to the terminal. It was pretty easy. I like that the fact that this port is closer than Galveston, but I do see parking being a problem when you have 2 or more cruises ship leaving from Bayport. I think Galveston has a lot more parking available.
Also, we arrived around 1230pm and were in our cabin by about 1250pm, but again, there was no other cruises embarking or debarking, so it was a piece of cake.
I would just be sure I got there early and have patience. Enjoy your cruise.
Tina