(Reposting from a thread started by a member planning an Amtrak trip to Galveston in order to catch a cruise ship.)
I am a semi-regular volunteer at the Galveston Railroad Museum, which is located in the former Galveston Union (railroad) station. It also serves as the Galveston terminus for the Thruway bus to Houston, Nacogdoches and Longview which connects to/from the Texas Eagle. Amtrak passengers are welcome to wait inside and use the restrooms in the museum during operating hours (normally 10a-5p summer and weekends; 9a-4p weekdays in the off-season). We have many passengers connecting to and from cruise ships; one terminal is literally a block away from the museum while the other terminal (which Royal Caribbean normally uses) is about three or four blocks farther away. The bus drivers are generally familiar with the needs of cruise ship passengers and I've never heard of someone being left.
The "24 hour advance notice" applies mainly to last-minute passengers; they need to make sure that the drivers know to expect you. If you have made your reservations in advance you do not need to reconfirm from the ship; you will be on the driver's manifest. When connecting southbound from the Texas Eagle you should be able to check your luggage "through" but you will need to claim it in Longview and put it on the bus for the trip south. Traveling north from Houston I have always been able to check my luggage but originating in Galveston you will probably not have the opportunity to check it in either Houston or Longview due to the 45 minutes before departure check-in requirement.
Have a good trip, and if you have a few extra minutes to spend the collection at the Galveston museum is worth the price of admission. Enjoy!
A few more thoughts....
The Houston/Galveston throughway bus is a full size, restroom equipped intercity bus. The times I have ridden it the driver played (forgettable...Paul Blart Mall Cop?) DVD movies. (OK, so National Treasure 2 wasn't so bad....) The stop in Nacogdoches is made at a truck stop and is generally about 20 minutes long; long enough to visit a real restroom and pick up some refreshments for the remainder of the trip. The stop in Houston is made at the Amtrak station; while there isn't much in its vicinity there are restrooms and vending machines if you just must have something more to snack on. (Make sure that the driver knows you'll be in the station....)
The museum/bus stop in Galveston is located at the head of The Strand, a very popular historic district with a number of bars, shops, cafes, and restaurants. It's safe and walkable day and night. My own "must-see" on The Strand, aside from the Museum, is La Kings Confectionary two blocks up the street...an old-fashioned ice cream parlor and candy factory which makes the best banana splits and ice cream sodas in town.
If you decide you would like to spend a night in Galveston before or after, the Tremont House is just two blocks from the Museum. It's an upscale Wyndham property; a bit pricy but very nice inside. Their rooftop bar overlooking the harbor is "not to be missed" if you're in town at sunset.
For lunch I always recommend Star Drug Store a few blocks south of The Strand on 23rd St. While no longer a working pharmacy, it does have its original old-fashioned lunch counter serving sandwiches, burgers, and ice cream treats which rival La Kings.
If you make a day of The Strand, be sure and stop in to see Galveston's "tall ship", the 1877 sailing ship Elissa.
The Galveston beaches are always attractive but you will need transportation to them from The Strand. If you are staying at the Tremont House or its sister properties the Harbor House or the Hotel Galvez there is a shuttle van which runs between them, but on a rather irregular schedule. (Hotel Galvez is just across Seawall Boulevard from the beach.) Otherwise you're looking at a taxi or renting a car.
If you do rent a car consider a visit to Moody Gardens, which is a destination resort towards the west of the island with a number of attractions. It's also very close to Schlitterbahn Galveston, a major water park.