With regards Air Ecosse, the remains were purchased by Peregrine/Aberdeen Airways in the mid to late 80's, however Aberdeen Airways eventually went bust, in the early 90's.
The only link between Aberdeen Airways and Business Air was that Business Air picked up a few routes and night mails and a few staff when Aberdeen Airways went bust. Several of the Aberdeen Airways staff still work with bmi regional today.
Business Air itself has an interesting history. Although it's origins came about in the very early 80's, it was Ian Woodley and Graham Ross (with a few other individuals) who 'bought' the operation in 1987 and turned it into an schedule airline, that was eventually purchased by British Midland in April 1996. Over the next five years it went through a couple of identity and organisational changes to appear as bmi regional in 2001.
Despite all these changes, bmi regional still has a number of staff from the early days of Business Air, one of whom is now the MD of bmi regional.
One last point is that Business Air/bmi regional has always held its own AOC.