Developed a lump after breaking my nose at the bridge. What could it be?

Of course, this is difficult to know without photos and exam, but because you can flatten it and because it returns slowly it may just be inflammation/swelling. It could be a small pice of bone/cartilage though, in my opinion, lass likely so. At any rate, an initial exam by a plastic surgeon possibly followed by another exam a few weeks/months later should help identify the cause and the treatment options----IF it persists.

Nasal trauma can cause a fracture of the nasal bones with and without displacement of them. Trauma can also cause cartilage in the nose to be fractured off of the nasal bones. Anytime there is trauma to the nose, a callous formation can occur at the site of the injury. If this is permanent,  then a hump removal is performed at the time of your rhinoplasty. 

Swelling, particularly at the bridge of the nose, is a common result of nasal trauma, whether or not there is an actual fracture.  Initially, it is important to use ice and elevation, just like in any other broken or bruised bone.  Early swelling that can be compressed, as in your case, will at least partially resolve.  However, pressure taping will help it resolve more quickly and more completely.  If the swelling persists and becomes firm, scar tissue has developed.  A small injection of steroids should help some.  Frequently, however, this scar tissue becomes permanent and requires surgical correction.