The correct answer is D) reckless.
The word that gives the reader a clue that Herodotus had a bias is "reckless."
When Herodotus writes that "For the Greeks, reckless of their own safety and desperate..." he is biasing the story because "reckless" is an adjective he is adding to the story in order to create some drama and highlights the moment so the reader can feel the emotion of the moment.
Herodotus, the Greek historian, is talking about one of the bloodiest battles of ancient Greek times: the Battle of Thermopylae.