Does having Bluetooth enabled draw extra power when no devices are connected?
Yes.  When the Bluetooth radio is active it not only turns on the receiver (which consumes power) but also periodically transmits to see if any known devices are in range.

When paired devices are on and within range, they do communicate occasionally even if not being used, and thus consume some power.

Turning off Discoverable will save some energy as it transmits less frequently than when it's not discoverable.

However, Bluetooth is such a lower power communications standard that it's hardly worth worrying about - active Bluetooth use (headsets in particular) do use a noticeable amount of power, but almost any other use, or just leaving it on, is negligible.

Further, for iOS devices the Bluetooth is often part of the RF chipset, and turning it off doesn't have much impact because it shares resources with the other RF functionality of the device, and without turning the other radios off (Wifi, GPS, cellular, nike+, etc) very little actually turns off when you disable Bluetooth.