He was forced to ask for their help 'on bended knee'. [=he was forced to beg for their help; he was forced to ask for their help in a very humble way]
If you want to clean the floor properly, you have to 'get down on your (hands and) knees' [=you have to kneel down on the floor] and start scrubbing.
She 'dropped/fell/sank to her knees' [=she knelt down] and begged for forgiveness. = She 'got down on her knees' and begged for forgiveness.
(..) That's her decision. She is the queen. I'm sorry it came to this. And your sisters? Do you see them bending the knee? My sisters will be loyal to the throne. Why do you think Sansa told me the truth about you? Because she doesn't want Dany (..)2019 TvShow: Game of Thrones Title: The Iron Throne Season: 8 Episode 6