Bluetooth Compliance
Here's the thing. There is no straightforward answer to this. You could sell your product without going through Bluetooth certification but you can't mention Bluetooth.

Marketing wise this is a bad idea. Are you goig to just say "Smartphone compatible"? How will customers k ow if it works or not? Seeing the Bluetooth logo is helpful.

There is a bigger issue here. When you use Bluetooth you are actually using patents of companies such as Nokia and others. They allow Bluetooth SIG and licensees to use it. The price for you is the Bluetooth Certification. I'm not a lawyer but technically you would be using patented technologies without a license. You could get sued. WI-Fi has a history of patent trolls suing, for example. Without certification you have no protection from the companies that provided their patents to the Bluetooth SIG. 

Besides this, if you are using a module, then the stack, PHY and controller are already certified. This means you are 80 to 90 percent done. You need to do (if I understand what you need and have) an end product listing. This costs a few thousands, but much less expensive than FCC and a full blown Bluetooth SIG for everything.

I think if you are selling a product, then marketing wise and other aspects, certification is advantageous. 

Get in touch with your FCC certification lab and ask about Bluetooth Certification. 
If you still need help, feel free to get in touch with me. My company helps clients with these issues exactly. 

By the way just because your module is FCC certified does not make your product certifird. You may want to go through unintentional radiator certification. Otherwise you are self certifying.