Where can I find a Bluetooth chip capable of shipping in bulk?
In mass production a BT chip costs less than 75 cents. The problem is none of the vendors will work with you, you need to find a module maker who can support you. In MP (Mass Production) you can reach to 5$ level with module including antenna etc. good luck. 

The key vendors to look at are CSR and BRCM (Broadcom). We use a Taiwanese module maker with one of their solutions. APMComm is the vendor, there are tons of others just look around.