&Map.get(&1, key)) gets translated into fn first_arg -> Map.get(first_arg, key) end where first_arg is &1.

So I guess that the &1 is not the bucket, so what it is?

&1 is the state of an agent and in case of your particular agent it is indeed the bucket (as a map). The error is probably due to you using the pid of the agent instead of its state.

iex(1)> {:ok, agent} = Agent.start_link(fn -> _bucket = %{} end)
{:ok, #PID<0.113.0>}
iex(2)> is_pid(agent)
true
iex(3)> is_map(agent)
false
iex(4)> bucket = Agent.get(agent, fn bucket -> bucket end)
%{}
iex(5)> is_map(bucket)
true
iex(7)> Agent.update(agent, fn bucket -> Map.put(bucket, :milk, 3) end)
:ok
iex(8)> Agent.get(agent, fn bucket -> bucket end)
%{milk: 3}
iex(9)> Agent.get(agent, fn bucket -> Map.get(bucket, :milk) end)
3
iex(10)> Agent.get(agent, &Map.get(&1, :milk))
3
iex(11)> Agent.get(agent, & &1)
%{milk: 3}