Dried herbs instead of bouquet garni?

There's nothing really special about a bouquet garni. Don't let the French name make this seem more intimidating than it is. It is just a bunch of herbs. It has no special function other than making the herbs easier to remove than if they weren't bundled together.

So then the meat of this question is really: can you substitute dried rosemary and dried sage for fresh rosemary and fresh sage in a bean soup?

The answer is: probably

Dried herbs can vary more in quality than fresh herbs, since it's possible that the dried herbs have been sitting around for a very long time. Very old dried herbs will have lost much of their flavor and should generally be avoided.

But if your dried herbs are relatively new, they'll probably be fine. Here's what Cook's Illustrated had to say about dried rosemary and sage:

In all but one application, tasters preferred fresh herbs to dry. Chili was the exception; in this dish, dried oregano was the favorite. A common criticism of dried herbs was that they had lost many of the subtleties and nuances of fresh herbs, tasting “dusty” and “stale.” Meanwhile, fresh herbs tasted “clean” and “bright.” Still, there were a few instances in which some dried herbs, though not preferred, were a passable substitute. In addition to oregano, dried rosemary, sage, and thyme fared reasonably well in recipes involving fairly long cooking times (more than 20 minutes) and a good amount of liquid.

https://www.cooksillustrated.com/how_tos/9261-science-substituting-dried-herbs-for-fresh

The recipe linked in the question calls for 18-20 minutes of cooking, which is slightly less than Cook's Illustrated recommends there. I'd be surprised if a couple of minutes made much of a difference, but if you're concerned, you could cook this soup for longer.