One of the complaints about BT in E60 is that it only supports very old phones. It might work intermittently with newer ones or no voice dial or address books can't be synced etc etc.
The CIP you can't find out yourself. Only the workshop can tell you. But yours is rather new, I will bet it's later than 13.2 which supports BT.
There seems to be correlation between some info in one of the hidden menu to the CIP.
Try this:
Turn on the key to get to the idrive.
1. Press and hold the knob for about 5-6 seconds
(If you didn't hold long enough, you will get into the normal vehicle setting etc menu instead)
2. Turn the knob clock wise 3 clicks
3. Turn the knob anti clock wise 3 clicks
4. Turn the knob clock wise 1 click
5. Turn the knob anti clock wise 1 click
6. Turn the knob clock wise 1 click
7. Press the knob again
You will see that you get into a secret menu on the i-drive screen. Look for something like "kontroller" and select it. Scroll to the last entry, you should see something like "E60 ... text... 500" If yours is more than 500 it's later than CIP 13.2 for sure.
If you have the legal screen, get pass it first before doing step 1.
BTW, if you pro-nav, this method won't work.