Thickness is not so much the issue as dryness; thicker work needs much more time to become bone dry. And, while the old trick of holding a piece to your cheek or seeing if it sticks to your tongue works for mugs, bowls, and similar thin-walled pieces, a thick sculpture may feel dry on the outside but still be wet on the inside of the wall. So, you need to give sculpture lots of time to dry.
Another key to firing sculptures is going slow . . . really slow on firing. Long pre-heat to make sure the piece is dry; slow increase of temperature to allow the piece to heat evenly while ramping up the temperature. During firing, your clay expands and contracts, so you also need to account for movement while firing -- especially if the piece has bulk and weight. Firing on a bed of grog, or on cookies/coils/etc. to allow the piece to easily move is a consideration.
Busts and objects should be hollow. When I fired sculpture pieces at the community studio, I preferred any paper, etc. on the inside be removed . . . yes, it is combustible and burns out, but it can make a mess inside the kiln . . . you don't want charred pieces of carbon left over from the sculpture firing floating onto a subsequent glaze fire load of functional ware. What you want to avoid is any carbon build up or oxidation on the elements; so if you do burn the paper, the next load should be a regular bisque or glaze that burn out any build up from the sculptural load.
Think about how you are going to fire the piece as part of your process of designing and constructing. Those who don't fire their own work often neglect to think about that part of the process.