What will it take to build a small bluetooth device?
There is an Atmel Bluetooth extension kit, and plenty of projects on other sites that describe interfacing Bluetooth with an AVR. You can also find tutorials for interfacing the AVR with a MicroSD card, so you could log all your data there.

SMT AVR chips are tiny and cheap. If you want to sacrifice size and price for faster development time, there is an Arduino Bluetooth module. Arduino is AVR based, so you can always cost/size reduce later down to your own custom design once you've got the bugs worked out.

Edit: Browsing Mouser, I found the TI CC2540, a bluetooth system-on-a-chip with an 8051 core.