Ok, not exactly a airline operating a BBJ, but rather one operating a Gulfstream I in reality (Idk when though). It's called Birmingham Executive, and according to "The Illustrated Directory of Modern Commercial Aircraft" by Gunter Endres, they used them on schedualed services regularly. Note that these planes are considered commercial aircraft too. I recall that Delta had a branch of themselves called Delta Select. I think they operated bizjets, though that was more for chartering a bizjet. I'm not too sure on this one. Note we also have Privateair who operates CJ319s. As for the 1970s argument? Well, look at it like this, did we have the same regulations we had in the 1950s? No, also, most of the aircraft at the time doubled in as biz planes, though they were more widespread amongst both sides. As Bizjets were introduced, it was found unfeasable for most airlines to use these as regular airliners, though there are a few airlines that operate these on routes. Not exactly your SQs and AAs, but a few.