You can walk to the station from many places in Bronxville. You can park at a resident meter space near the train, or obtain a long-term spot permit for specific parking lots. Here's a link to the Village's Office of Parking: Departments & Services: Parking - The Village of Bronxville
One thing to remember, Bronxville only allows front-in parking, not backing into spaces, and you can receive a ticket for that, even if you are legally parked by permit/meter. And, there is no on-street parking allowed at night; all vehicles must be in a residential lot or private driveway.