I'm not an expert on this, but here's a method that I've been able to successfully use to export objects from Bryce 7 Pro:

Assuming the model is actually a group of objects rather than a single object, you first have to check the attributes of each object in the group & make sure it's either positive or negative (not neutral). Once all the objects are changed in this way, a C should appear at the bottom of the selectable items for the group when the group is selected (see attached figure). Click on the C to Collapse the group. Once it's collapsed, the Export Object menu choice should no longer be grayed out & you can export it.

"Every child is an artist. The problem is how to remain an artist once we grow up." - Picasso