I think that Bryce aligns the object's Z-axis along the path. Your object apparently has the Z axis facing the wrong way.
Don't worry. You just need to use a null object. Create a cube and position it so that it's Z-axis is aligned along the path. Link it to the path. Now link your model to the cube. When you move the cube along the path, the model will go along for the ride. (remember to shrink the cube down so that it's hidden inside your model.)

Rubycon