I just ran into this issue, too. After picking up the bust, I put it in each of the nooks, then put it back on the plinth, at which point it disappeared. Changing reels doesn't do anything. Like Hassat Hunter said, the trip plate also disappears, but I'm pretty sure I made the bust disappear before I got the ventriloquist dummy or got any curses.
Here's my savegame:
http://www.mediafire.com/download.php?ydzm3yjmjzz
Unfortunately, I progressed a while after it happened, thinking it would reappear, so it might not help.
edit: I did a little more testing, and it has something to do with the right niche. If you put the bust in the right niche, the trip plate disappears. You can see this if you run over to the trip plate after placing the bust in the niche, or while you're removing the bust. After you remove the bust, the trip plate reappears, but I can't recreate this bug so I'm not sure what's causing the trip plate to stay hidden.