Bluetooth headsets are generally not recommended for use with any application that uses the microphone. That is not specific to VoiceAttack.
Many Bluetooth devices don't support a profile (basically, mode of operation) in which both the microphone and high-quality audio playback can be used simultaneously (this is not necessarily a matter of price, brand, or perceived quality, either).
Chances are that the device you're now using for playback will result in lower fidelity audio (which may or may not be an issue, to you personally).