Hi Mike,
it depends what kind of product you want to give as bonus. Most affiliate marketers use downloadable products such as ebook or software. If you want to give physical product of ebook or software in a CD or DVD then, I think the best service is KUNAKI as suggested by Joe. You can design your cover and managed the content on your own desktop and send to them to be burned to CD or DVD and make them delivered to your customer on your behalf.

But if you really want to dropship your product, you can consider DOBA at www.doba.com.
This site allow to order the product directly from the site without contacting each of providers.

If you want to know the list of a very reliable dropship provider then you should check WORLWIDEBRANDS as suggested by Debbie or SALEHOO at www.salehoo.com.

I have an account with WB and very satisfied with the reliable info they provided.