Great question Emma, there is a way to solve this! You're already halfway there by adding your products. For any other users who need help with this, Click Here for a guide. 

Now that you have your products added, to sell a product to a client without an expiration date or calendar event, and to ensure that it is included on your automated billing, navigate to the client card, and click on New in the top left. Then, click on Product and select your product as normal. This will add the charge for the product to the client's account right away. Also, as long as you don't invoice for the product, it will be included on your automated billing. Remember that automated billing automatically creates an invoice for any un-invoiced charges on a client's account. You also still have the option to create an invoice right away for this product if desired, or add these products to your clients' invoices as you create them. 

Click Here for a guide to adding a product to a client's account. Thank you for your post, please leave a comment here if further clarification is needed!