I think "bending down" could involve a knees bend. In the end, it's just
a way of looking at the action. "Bending down" emphasises the downward
movement rather more than "over", although "She bent right over" is
pretty extreme. On the whole, I think I mainly use "over" as a
preposition with "bend", as in "He leant over the rail", but "He bent
down to pick up the coin". Or "bent over" to indicate more a sideways
movement: "She bent over towards me and whispered in my ear".
--
Robert B. born England a long time ago;
Western Australia since 1972