For reference this is the info copied from the Device Properties.  Just so we have it in one place.  There's a lot of garbage in here but there's also a lot of IDs that could be helpful.

Device Description:
Bluetooth HID Device

Hardware IDs: 
BTHENUM\{00001124-0000-1000-8000-00805f9b34fb}_VID&0002057e_PID&0330
BTHENUM\{00001124-0000-1000-8000-00805f9b34fb}_LOCALMFG&0045

Compatible IDs:
BTHENUM\{00001124-0000-1000-8000-00805f9b34fb}

Service:
HidBth

Device Class:
HIDClass

Device Class GUID:
{745a17a0-74d3-11d0-b6fe-00a0c90f57da}

Driver Key:
{745a17a0-74d3-11d0-b6fe-00a0c90f57da}\0019

ConfigFlags:
00000000

Manufacturer:
Microsoft (lol wut?)

Physical Device Object Name:
\Device\00000098

Capabilities:
00000084
CM_DEVCAP_REMOVABLE
CM_DEVCAP_SURPRISEREMOVALOK

Enumerator:
BTHENUM

Power Data:
Current power state:
D0

Power capabilities:
00000009
PDCAP_D0_SUPPORTED
PDCAP_D3_SUPPORTED

Power state mappings:
S0 -> Unspecified
S1 -> Unspecified
S2 -> Unspecified
S3 -> Unspecified
S4 -> Unspecified
S5 -> Unspecified


Removal Policy:
00000002

Removal Policy Default:
00000002

Install State:
00000000

Base Container ID:
{b3dc97b4-e280-5814-8b80-c46072f8c16b}

Display Name:
Bluetooth HID Device

Device Instance Path:
BTHENUM\{00001124-0000-1000-8000-00805F9B34FB}_VID&0002057E_PID&0330\7&2977C862&0&58BDA34FC666_C0000001C

DevNode Status:
0180600A
DN_DRIVER_LOADED
DN_STARTED
DN_DISABLEABLE
DN_REMOVABLE
DN_NT_ENUMERATOR
DN_NT_DRIVER

Problem Code:
00000000

Parent:
BTH\MS_BTHBRB\6&2225fe9&0&1

Siblings:
BTHENUM\{13b67e97-545b-41dc-ac44-6fede5fe6087}_LOCALMFG&0000\7&2977c862&0&000000000000_00000000
BTHENUM\{61118058-486c-4bb0-b4b8-ace4dcadec44}_LOCALMFG&0000\7&2977c862&0&000000000000_00000000
BTHENUM\{8855c1d2-9bfe-4b96-bcbf-cbb9682c76bd}_LOCALMFG&0000\7&2977c862&0&000000000000_00000000
BTHENUM\{cbecab40-a2c8-4ab3-adc1-de0fe95d8600}_LOCALMFG&0000\7&2977c862&0&000000000000_00000000

Container ID:
{b3dc97b4-e280-5814-8b80-c46072f8c16b}

Safe Removal Required:
false

Bluetooth Device Address:
58BDA34FC666

Bluetooth Service GUID:
{00001124-0000-1000-8000-00805f9b34fb}

Bus Reported Device Description:
Bluetooth Peripheral Device

Unpair Uninstall:
true

Always show the device as connected:
true

Device Node not indicitave of device presence:
true

Driver Node Strong Name:
hidbth.inf:MicrosoftHid.NTamd64...1:HIDBTH_Inst:6.1.7600.16385::bthenum\{00001124-0000-1000-8000-00805f9b34fb}

Install Date:
12/7/2011 10:11:23 PM

First Install Date:
12/7/2011 10:11:23 PM

Driver Assembly Date:
6/20/2006 4:00:00 PM

Driver Assembly Version:
6.1.7600.16385

Driver Assembly Description:
Bluetooth HID Device

Inf Name:
hidbth.inf

Inf Section:
hidbth.inf

Inf Section Extension:
.NT

Matching Device ID:
bthenum\{00001124-0000-1000-8000-00805f9b34fb}

Provider:
Microsoft

Rank of Installed Driver:
00FF3000

Included Infs:
input.inf

Class Long Name:
Human Interface Devices

Class Short Name:
HIDClass

No Install Class:
true

Class Icon Path:
%systemroot%\system32\setupapi.dll,-24

Display Name:
Human Interface Devices