Our cruise has been moved from New Orleans to Houston. Does anyone know how to get to the port from Bush Intercontinental Airport and how much it might cost? Is it possible to rent a car and drop it off near the pier?
Also, we will be travelling with an infant (8 months) and will need to shop for diapers, formula and baby jar food for the cruise. Is there any supermarkets near the port? Any help will be greatly appreciated.

Check out this page:

http://www.portofhouston.com/cruisei...eterminal.html

There is no car rental agency at the cruise terminal. But there's $7/day parking. There's no supermarket near the terminal, nor are there any major supermarket chains along the way from IAH to the Port of Houston. You have to make some detour to other parts of town to find one.

The cruise terminals are also outside the fare zones of taxis from IAH, so you need to find out how much first.

Can you arrange transfer from the cruise company? That'd be the best way. Otherwise,

Just curious - is Port of Houston different from Galveston?

Yes

Two different cities.

I figured Galveston Limo might have a shuttle to Port of Houston, but apparently they only service Port of Galveston for cruisers.