Tackled this project last weekend.
Turns out that a spade terminal had broken on the bulb socket...
Parts picked up were the luminous/orange ring, bulb and bulb socket.
Turns out that the bulb socket (from MINI) INCLUDES the bulb. (returned today)
Ended up breaking the spade terminal, again, during reinstallation. Probably too much movement. Since I had everything reassembled, I just decided to install an unused LED. pretty simple, just wired into the small holes in the connectors for the cigarette lighter. The LED sat nicely between the cup holders (under) and lights up the ring whenever car is on.
If I had to do it again, which I probably will...I would oder some orange, maybe, two flush mount LEDs, (Little Dot SMD), from superbrightleds.com and aim them/tape on the ring...

 

Nice tips.
Those things are a pain to fix/extract.

After replacing my front one, I just sheered off the one in my boot (who's idea was it to have it protrude in a cargo area anyway?)