Bangle & Arduino communication through Bluetooth?

Which characteristic are you trying to read from? Battery level?

I think what you need is startNotifications - there's a bit of code in the reference: http://www.espruino.com/Reference#l_BluetoothRemoteGATTCharacteristic_startNotifications

It looks like there might be a UART characteristic there, and to use that the code above can be used pretty much as-is.

But for battery I think something like this might do it:

var gatt;
NRF.connect("pu:ck:js:ad:dr:es random").then(function(g) {
  gatt = g;
  return gatt.getPrimaryService(0x180F);
}).then(function(service) {
  return service.getCharacteristic(0x2A19);
}).then(function(characteristic) {
  characteristic.on('characteristicvaluechanged', function(event) {
    console.log("battery: "+JSON.stringify(event.target.value.buffer));
  });
  return characteristic.startNotifications();
}).then(function() {
  console.log("Done!");
});