If a creature is blocked but Trample damage is still done to a player, this damage can't be redirected to the Bodyguard because the Bodyguard only takes damage from unblocked creatures.

Damage goes to the Bodyguard as long as he is untapped. This works even if he is blocking.

If you have multiple Veteran Bodyguards, you can decide which one receives the redirected damage each time damage would be dealt to you.