Praise be to Allah.
Firstly:
If the bank buys a car from you then sells it to the customer, and it gives you 500 dollars in return for referring the customer to the bank, there is nothing wrong with that. It comes under the heading of combining the brokerage and sales contracts. It does not matter that the bank is non-Islamic if it is going to buy a car from you and then sell it to the customer.
But if the role of the bank is to provide finance and pay on behalf of the customer without buying a car from you, then this in fact is a riba-based loan which is haraam: the bank lends the customer money so that he will pay it back with something extra added. In that case it is not permissible to refer the customer to the bank, and it is not permissible for you to take anything from the bank, because guiding people to that which is haraam is not permissible.
See the answer to questions no. 113945 and 119229.
Secondly:
It is permissible to sell the car to the riba-based bank which will sell it to the customer, because legitimate transactions with those who deal in riba are permissible. Hence the Sahaabah (may Allah be pleased with them) dealt with the Jews, buying and selling and the like, even though the Jews engage in riba.
And Allah knows best.
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