"When receiving Holy Communion, the communicant bows his or her head before the Sacrament as a gesture of reverence and receives the Body of the Lord from the minister. The consecrated host may be received either on the tongue or in the hand, at the discretion of each communicant. When Holy Communion is received under both kinds, the sign of reverence is also made before receiving the Precious Blood."
[No. 161] "If Communion is given only under the species of bread, the priest raises the host slightly and shows it to each, saying, 'Corpus Christi' (The Body of Christ). The communicant replies, 'Amen,' and receives the Sacrament either on the tongue or, where this is allowed and if the communicant so chooses, in the hand. As soon as the communicant receives the host, he or she consumes it entirely."
The text does not specify the moment of this bow of reverence and there are few other specific norms. The original text does not specify a bow but merely refers to an act of reverence to be established by the bishops' conference. Some conferences have included the option of making either a genuflection or a bow.
In practice the act of reverence may be made either just before receiving or while the person immediately before oneself is receiving. It really depends on the number of communicants.
A small intimate group of faithful can easily make the gesture just before receiving the sacred host. But if this gesture, although lasting no more that a few seconds, were to be repeated hundreds of times in a large parish, then the rite of Communion could be unduly prolonged. This practical reason probably motivated the recommendation to perform the gesture of reverence while the person in front is receiving Communion.
Does this mean that I am really bowing to the person in front of me? Personally I think not, because one naturally reverences a person turned toward oneself and practically never performs an act of respect toward a person who has his back turned away. Thus the natural direction of the act of reverence is toward the Eucharistic Christ.
Finally, this question offers an opportunity to remember the norm that the Eucharist must be consumed immediately and before the priest, deacon or extraordinary minister of Holy Communion.
In general, it is necessary for priests to remind the faithful of this requirement from time to time, and to insist on its being fulfilled so as to avoid unfortunate incidents due to distraction or even willful profanation of the Eucharist. ZE05101122