Ziba is not literally bowing before the king when he is speaking here. This means that he will serve the king with the same amount of humility he would be showing if he were literally bowing before him. Alternate translation: "I will humbly serve you" (See: [[rc://en/ta/man/translate/figs-metaphor]])
The phrase "find favor" means to be approved of by someone. Also, "eyes" is a metonym for sight, and sight represents judgment or evaluation. Alternate translation: "I want you to be pleased with me" or "I desire you for to be pleased with me" (See: [[rc://en/ta/man/translate/figs-idiom]] and [[rc://en/ta/man/translate/figs-metonymy]] and [[rc://en/ta/man/translate/figs-metaphor]])