Rounded nose bridge? Is there a way where one would be able to place a thin, narrow piece of rib on top of the bridge to avoid t

The simple answer to your question would be yes indeed it is possible. Most of the time it is not necessary since the shape that you described can also be achieved through the reshaping of the bridge. You are referring to preservation or creation of visible dorsal aesthetic lines.
This takes different approaches depending on whether the bridge is reduced or built up.
The most common situation that ends up with a wider and more rounded contour of the bridge tends to be a hump reduction.
When the bridge of the nose is reduced, ultrasonic instruments can be very helpful to create slender and more angular appearance of the bridge if required.
When the bridge projection is built up, it can be carried out by an onlay of rib cartilage, diced cartilage or elevated spreader grafts. 

In reality, there are significant differences in nasal dorsum presentation. There is no single aesthetic standard that is applicable to all noses and all patients. This aspect of nose is something that needs to be carefully evaluated and discussed with patient before surgery as well as it's relation to the nose tip in particular. This issue is best addressed in direct communication with your surgeon possibly supported with 3 D simulation if available. Good luck.  

I try to avoid rib grafts in most rhinoplasties. I recommend going on a few consults to see if a rib graft is even necessary in your situation.

 Its probably best that you make sure to look at before-and-after pictures that are at least six months to year after the rhinoplasty procedure and then make your determination, since the bridge line will look round and puffy for the first few months after the procedure. This is due to normal swelling. Nasal cartilage is always the primary grafting source for cartilage grafts when they are required to be placed across the bridge of the nose. Not rib cartilage.

One of the most complex aspects of rhinoplasty’s making the bridge of the nose look straight and narrow. Often if there’s a large hump beforehand, flattening the nasal bridge can actually make the boundaries of the nasal bridge looks slightly wider. An experienced surgeon can narrow the nose with a combination of cartilage grafts and bone reshaping maneuvers. On a primary rhinoplasty rib graft really needs to be used except and very specific circumstances.