I’m assuming the reason its hard to find articles about this method is because its simply dangerous at a common-sense-type level, so no one is doing it. You’ll notice that the articles you do find are on personal blogs and not in journals.
What if someone doesn’t have the dynamic stability and falls of the bike? Drops a weight on the wheel or foot? Slips off a pedal? They’re going to get hurt.
Any instructor at any level with any education at any respectable facility knows that safety comes first, and will always remain the top priority.
I found this article for you hoping this will help
While I was looking for it I came across a video of such a class on this blog http://funhogspins.blogspot.com/2008/05/aerobics-on-bike.html
Looks like there are spinning classes that are also incorporating resistance bands too!
Let’s hope you can educate this instructor before someone gets hurt!!