Reply just done this on my 2001 E39 530D Touring.

Only three mods to the OP method;

1. To release the connection - first hold the connection fully down that makes sure that the clips aren't being pinched in place, The clips then easily squeeze using circlip pliers or long-nosed pliers, then lift the connection free of the airbag, even after 21 years the clips weren't at all brittle;

2. Having removed the bottom retaining bolt I had to use a hammer and a drfit in the bolt hole to free the bag from its seat;

3. When reconnecting the airbag give the connection a good thump with your palm to make sure that it is properly seated, the left one pushed home easily enough the right one wouldn't push home until there was weight on the suspension.