Can I pay my car insurance out of someone else's bank account?

The customer service agent will want to speak to the person who owns the bank account. For direct debit, usually a form will be sent through the post which needs to be signed by the bank account holder so that monthly deductions can be authorised. If you're paying the premiums in full, the person whose bank account this is will have to speak to the representative and confirm certain details like name, address and CCV number on the back of card.

For applications made online, usually there's a "Verified by Visa" prompt which needs to be filled in as an added security measure.

Whose bank account are you trying to use?

My monthly installments for car insurance goes out of the Missus account, so if you were looking to do the same, you wouldn't have any problems.