最初に結論

Package.appxmanifest を編集してBluetoothの機能を使う設定にしてください。

BluetoothLEAdvertisementWatcher

https://docs.microsoft.com/en-us/uwp/api/windows.devices.bluetooth.advertisement.bluetoothleadvertisementwatcher
このクラスのReceivedのイベントにコールバックを登録すると、周辺でアドバタイズ中のBLEデバイスの情報を随時取得できます。

実装例

var BleWatcher = new BluetoothLEAdvertisementWatcher 
{ 
    ScanningMode = BluetoothLEScanningMode.Active
};

BleWatcher.Received += async (w, btAdv) => {
    var device = await BluetoothLEDevice.FromBluetoothAddressAsync(btAdv.BluetoothAddress);
    Debug.WriteLine($"BLEWATCHER Found: {device.name}");

    // SERVICES!!
    var gatt = await device.GetGattServicesAsync();
    Debug.WriteLine($"{device.Name} Services: {gatt.Services.Count}, {gatt.Status}, {gatt.ProtocolError}");

    // CHARACTERISTICS!!
    var characs = await gatt.Services.Single(s => s.Uuid == SAMPLESERVICEUUID).GetCharacteristicsAsync();
    var charac = characs.Single(c => c.Uuid == SAMPLECHARACUUID);
    await charac.WriteValueAsync(SOMEDATA);
};

BleWatcher.Start();