Itachi wrecks Bee. Canonically, Naruto stated that Bee and himself shouldn't be able to fight off Amaterasu and Tsukuyomi. Then we have Yagura's example, who was a perfect Jinchuriki as well. Then there is a factor of Substitution or Kawarimi, which can only work if Bee uses it before Amaterasu hits him. Which would explain why he couldn't do so whilst covered in Flames.
Itachi was also fast enough to engage in CQC with Bee and Naruto in KCM, so in close ranged Combat, avoiding Itachi's eyes would be impossible as well.