As the bell in its hanging from ceiling state has a 2x2 top, it should be able to be placed on the bottom of any solid block whose base is flush with the bottom of a block and has at least a 2x2 area on the bottom. However, this does not actually happen, and placement completely refuses. However, lanterns can be placed on the bottom of all of these blocks, while having a chain that takes up a 2x2 area.
Affected blocks (many more blocks in invalid positions may also be affected):
Fences
Walls
Glass panes
Iron bars
End rods, when facing up or down
Hoppers, when facing down
Chests
Grindstones, when facing down
Brewing stands
Flower pots
Heads
Chains
Chains are affected too.