On 21st June 2017, MIT announced the release of a new version of their BLE extensions for AppInventor: iot.appinventor.mit.edu
As well as a completely revised set of general BLE functions, the release also includes a specific set of functions for the BBC micro:bit and the Arduino101 in which the Device Specific Service and Characteristic UUIDs are already built into the functions and therefore hidden from the user - so much simpler!
I spent a lot of time trying to get the original version of the BLE extension (released last year) to work with the micro:bit - it was tortuous and not everything worked! I was lucky enough to get asked to help beta test the second version and did find a couple of bugs!
Virtually everything you might want to do over BLE with the micro:bit is now fully supported (I can't comment on Arduino101 support because I don't have one) - all you need to do is load the the relevant extensions: BLE, Microbit, and Arduino101 into your AppInventor project and off you go.
I intend to publish a some tutorials on my blog, if anyone is interested.
Great stuff Neil - if you could share the tutorials here we'd love to see and share them.