By 1963 a radio in the dashboard of a car was very common. Why would someone listen to a transistor radio and run down the batteries inside it, when they had the option of simply using the car radio?
Well, we do not know what Toni meant. Maybe they had both, in car and transistor one. Common sense says, OK, they were listening the car radio while they were driving and once they parked the car (probably not too close to Dealey plaza) they took transistor and listened the progres of the motorcade. In any case, appart from radio issue not being clear, this person position in Bell film coresponds to Toni statemen about her husband.