This goal will nearly always be done with a Village. Villages can be located by using the Pie Chart to look for Bell. You can punch a Bell or its supporting block to obtain it, and Pickaxes mine it faster. This table shows the time you save by breaking the supporting block over the bell. Note that negative times means that you should have broken the Bell instead.
Below is shown the meeting points for each village type and the quickest way to get the Bell with no tools:
Punch Cut Sandstone (4s)
Punch Bell (7.5s)
Punch Bell (7.5s)
Punch Bell (7.5s)
Punch Bell (7.5s)
Punch Oak Planks (3s)
Punch Bell (7.5s)
Punch Wool (1.2s)
Punch Oak Planks (3s)
Punch Grass Block (0.9s)
Punch Terracotta (6.25s)
Punch Acacia Slab (3s)
Punch Acacia Slab (3s)
Punch Packed Ice (0.75s)
Punch Spruce Planks (3s)
Punch Spruce Wood (3s)
Punch Spruce Planks (3s)
Punch Spruce Log (3s)
When you have tools, it changes a bit. Smooth Sandstone and Cobblestone become quicker than the Bell to break with a Pickaxe.
Wood remains quicker to punch than mining the Bell even if you have a Wood Pick, unless you have a Stone Pick and no Axe.
Savanna, Snowy and Taiga villages will never have you punching the Bell.
See the provided table for the quickest block to break per supporting block.
Rarely, Ruined Portal chests can contain a Bell. The chance of this happening for any given chest is 1.5%, meaning 1 in 67 Ruined Portals will have a Bell.
This is the nichest situation, but if you have an Igloo, somehow plenty of emeralds and absolutely no Village nearby, you can level up a Toolsmith or Weaponsmith to Apprentice to unlock a trade of a Bell for 36 Emeralds. You can do the same with an Armorer, but the trade is not guaranteed like it is for the other two. Of these, Toolsmith would probably be best for levelling up cheaply.