I suggest you start a dialogue with your employers around safe guarding, being alone with students and off site. Explain that you are uncomfortable about it and would like to help develop a best practice policy.
If that doesn't work or move things forward, then simply refuse to do it. Create all sorts of complications around your car and how you had to get the bus today etc, then ask for a taxi to take yiu and the student to the destination, the taxi driver being the third person in the car which makes for a more appropriate solution.