Remember, 'bluff into doing' implies the speaker intentionally deceived someone to achieve a goal. He bluffed her into doing his homework, making her think it was a teamwork assignment.
Pro Tip 2/3
Not Literal
'Bluff into doing' doesn't mean the person actually has the power or means they claim to have. The older kids bluffed the younger ones into doing their chores, saying they'd summon a ghost otherwise.
Pro Tip 3/3
Informal Context
The phrase is used in informal situations and may be inappropriate for formal or serious contexts. She bluffed him into doing the presentation, joking she'd reveal his secret love for karaoke.