Is there a way to limit the number of MicroStation instances a user can open?

I dont know how familiar you are with Configuration variables, how there processed, and macros but did have an idea that you could try to implement:

By using config variables and macros you could set up the above so that the first session on a machine opens files normally but subsequent sessions on the machine would be forced to open files as read only until the first session is closes.

There is a built in variable MS_READONLY that forces files to open read only.

a couple articles that could help you would be:

https://communities.bentley.com/products/microstation/w/microstation__wiki/2834/configuration-variable-processing

https://communities.bentley.com/communities/other_communities/askinga/w/askinga/1109/run-a-vba-macro-when-opening-or-closing-design-files

https://communities.bentley.com/products/microstation/w/microstation__wiki/13825/how-to-define-a-variable-using-a-key-in

https://communities.bentley.com/products/microstation/f/z_-archived-microstation-v8i-forum/83439/configuration-variable

Something like this might work. I will look into it more when I have time. 

Something like this might work. I will look into it more when I have time.