I am not aware of any specific rubrics for the reader to follow when approaching the ambo to proclaim the readings. I think the GIRM is clear that the reader doesn’t genuflect–not during the Mass itself. Of course, the GIRM doesn’t say that the reader bows, either. (posted below).
I’ve been told (by both my bishop and rector) that the theology of the Novus Ordo Mass is based upon the altar as the body of Christ. During Mass, we don’t ignore the tabernacle, but the attention is upon the altar of sacrifice, as the body of Christ. If you’re familiar with the Usus Antiquor, you know that the altar is crowded with stuff–books, chalice, candles, flowers, altar cards, etc. In the Novus Ordo Mass, nothing is on the altar unless it’s being used right now.
It makes good sense, if during Mass the altar of sacrifice is the body of Christ, that we reverence the altar with a bow and not the tabernacle.
Here’s the GIRM section:
Genuflections and Bows
- A genuflection, made by bending the right knee to the ground, signifies adoration, and therefore it is reserved for the Most Blessed Sacrament, as well as for the Holy Cross from the solemn adoration during the liturgical celebration on Good Friday until the beginning of the Easter Vigil.
During Mass, three genuflections are made by the Priest Celebrant: namely, after the elevation of the host, after the elevation of the chalice, and before Communion. Certain specific features to be observed in a concele-brated Mass are noted in their proper place (cf. nos. 210-251).
If, however, the tabernacle with the Most Blessed Sacrament is situated in the sanctuary, the Priest, the Deacon, and the other ministers genuflect when they approach the altar and when they depart from it, but not during the celebration of Mass itself.
Otherwise, all who pass before the Most Blessed Sacrament genuflect, unless they are moving in procession.
Ministers carrying the processional cross or candles bow their heads instead of genuflecting.
- A bow signifies reverence and honor shown to the persons themselves or to the signs that represent them. There are two kinds of bow: a bow of the head and a bow of the body.
a) A bow of the head is made when the three Divine Persons are named together and at the names of Jesus, of the Blessed Virgin Mary, and of the Saint in whose honor Mass is being celebrated.
b) A bow of the body, that is to say, a profound bow, is made to the altar; during the prayers Munda cor meum (Cleanse my heart) and In spiritu humilitatis (With humble spirit); in the Creed at the words et incarnatus est (and by the Holy Spirit . . . and became man); in the Roman Canon at the Supplices te rogamus (In humble prayer we ask you, almighty God). The same kind of bow is made by the Deacon when he asks for a blessing before the proclamation of the Gospel. In addition, the Priest bows slightly as he pronounces the words of the Lord at the Consecration.