Bluetooth headsets work great with the 1062. No OBiBT needed with the 1062. I use my OBi1062 with 3 different headsets:
1) Plantronics Voyager Legend
2) VXi Blueparrott B450-XT (my primary daily desk headset now)
3) VXi Blueparrott Reveal Pro (primary headset for in the car)
The Plantronics can be a little flaky with the OBi1062. But both VXI headsets are rock solid and the buttons on the headset work for hang up/answer, mute and volume.
If you get an 1032 w/ OBiBT or a 1062, let us know which headsets you have luck with!