Why are we encouraged to bow during the Nicene Creed at the part where say “by the power of the Holy Spirit he was born of the Virgin Mary, and became man”? And why do some people bow earlier at “For us men and for our salvation he came down from heaven”?
Anticipation?

They’re early. The bow is for the words
Et incarnatus est de Spiritu Sancto ex Maria Virgine, et homo factus est only.
We bow at this part of the Creed as a sign of reverence for the wondrous miracle of the Incarnation, by which our God deigned to come to us as a man. The bow is just that: a sign of reverence for the Incarnation.
In
The Glories of the Catholic Church: The Catholic Christian Instructed in Defence of His Faith (via
Google Books), the explanation given is this:
Why does the priest kneel at the words
Et incarnatus est?
In adoration of our Lord’s blessed Humanity and in profound acknowledgment of His unspeakable condescension in taking our flesh upon Him.
In the Extraordinary Form of the Roman Rite, you
genuflect at this part of the Creed. You also genuflect when John 1:14 is read at the end of the Mass (“
et Verbum caro factum est et habitavit in nobis…”, “And the Word became Flesh and dwelt among us…”).
In the Ordinary Form of the Roman Rite, you
genuflect at this part of the Creed on only two occasions: the solemnities of the Annunciation (March 25) and of the Nativity (December 25). I’m not sure if, as
benedictgal said, the genuflection is also done during the
Octave of the Nativity of our Lord.