I had the same issue. I bought an IOGear bluetooth dongle and used it with a USB extension base
Works FLAWLESSLY. Even during intense gaming when both the Keyboard and mouse would get so laggy it was impossible to play. It even works better than it did during normal use when I didnt have the display plugged in.
Amazing results.
Extension: http://www.amazon.com/gp/product/B001K9BFB8/ref=as_li_ss_tl?ie=UTF8&camp=1789&cr eative=390957&creativeASIN=B001K9BFB8&linkCode=as2&tag=sharaw-20
Bluetooth Dongle: http://www.amazon.com/gp/product/B0018O9JIG/ref=as_li_ss_tl?ie=UTF8&camp=1789&cr eative=390957&creativeASIN=B0018O9JIG&linkCode=as2&tag=sharaw-20
One thing to check, OSX directions sucked, so do this.
1. Leave your bluetooth on, with all devices still configured/connected
2. Option Click the bluetooth icon on your menu bar
3. Write down the 'Address' listed. This is the address of your internal Bluetooth
4. Plug in the Extension and then the Dongle.
5. Wait a couple seconds
6. Option click the bluetooth icon again
7. Make sure a different address is shown. If so, you are now transmitting/recieving from the dongle and not the macbook.
8. I plugged the extension into my Thunderbolt display and now I can just unplug my macbook and go. All peripherals will still work as it autoswitches back to the internal bluetooth once disconnected.
Hope this helps