As you approach the station, there's a parking garage. You can also use the rewards parking location like the parking spot or fast park. They will drop you off and pick you up. You can park free at the Halethorpe Commuter Station that is one stop from BWI station. The round trip ticket on the MARC train will be way less than your parking fees.
There's a massive parking facility right across the strret from the BWI Amtrak station, you can't miss it.
In the adjacent parking garage.
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