Is there a way to have a response number automatically generated after a form is submitted?

I am looking to set up an online basket raffle. I need a way to keep track link the bid to winner and bis to payment.

You must be referring to the Unique ID field. Check out this user guide: 

How-to-Add-Custom-Unique-IDs-to-your-Form-Submissions

Let us know if you need further assistance.

would this give the number to them? 

Yes. You can include this number in the Autoresponder Email of your form. 

When users submit the form, they will receive a confirmation email (autoresponder) with the auto number in the email message content.