I'm planning on using an obd bluetooth reader on my car and leaving it plugged in to use apps like dash and torque. It's a daily driver so I'm not that scared of depleting the car's battery, but I was curious how much amperage that port would suck.
I am not sure of your exact solution, but Brian Blum of Texas Instruments says the amperage draw depends on what state the device is in, of which there are seven states. According to the document in the link, it draws as follows:
These are for the device listed in the document, but should be about the same. As you can see, these are very small amounts of draw. I would also bet, if you look at your device specs, when the vehicle is off, your device is off: no power consumption during this time. For your edification, it takes 1000 mA to make one (1) Amp.
NOTE: Because of a special character in the URL, the SE interface is not interpreting the above link correctly. Go to this Google Search and choose the pdf link which says: Bluetooth low energy, A Very Low Power Solution.pdf from Texas Instruments.