How can I check whether there is a bootstrap.js loaded on page (a file bootstrap.js may be compiled into another big JS file)?
All you need to do is simply check if a Bootstrap-specific method is available. I'll use modal in this example (works for Bootstrap 2-4):
// Will be true if bootstrap is loaded, false otherwise
var bootstrap_enabled = (typeof $().modal == 'function');
It is not 100% reliable obviously since a modal function can be provided by a different plugin, but nonetheless it will do the job...
You can also check for Bootstrap 3-4 more specifically (works as of 3.1+):
// Will be true if Bootstrap 3-4 is loaded, false if Bootstrap 2 or no Bootstrap
var bootstrap_enabled = (typeof $().emulateTransitionEnd == 'function');
Note that all of these checks require that jQuery is already loaded.