I agree that an ascii representation of a base 2 bigint is especially inefficient :)

Sine there is no machine native representation of a bigint that has an analog of a portable network order, why not use good old ascii? To make it more efficient, use a decimal or hexadecimal base (from the manpage):

# conversion to string (do not modify their argument)
         $x->bstr();    # normalized string
         $x->as_hex();  # as signed hexadecimal string with prefixed 0
+x

         # Number creation
         $x = Math::BigInt->new($str);         # defaults to 0
[download]

One could get double density with packed hexadecimals, but it would not be as human readable.