Stand as the bishop directs. I agree with his interpretation of the 2002 General Instruction of the Roman Missal (GIRM) approved for the USA, which can be accessed from
romanrite.com/girm.html :
“43. … They should, however, sit while the readings before the Gospel and the responsorial Psalm are proclaimed and for the homily and while the Preparation of the Gifts at the Offertory is taking place; and, as circumstances allow, they may sit or kneel while the period of sacred silence after Communion is observed. …”.
The period of “sacred silence” is not while the priest is saying “The body of Christ” to people. This is not silence. So the permission to sit or kneel does not apply to that time.
Rather than an approach of private prayer, try to go with the GIRM: “86. While the priest is receiving the Sacrament, the Communion chant is begun. Its purpose is to express the communicants’ union in spirit by means of the unity of their voices, to show joy of heart, and to highlight more clearly the “communitarian” nature of the procession to receive Communion. The singing is continued for as long as the Sacrament is being administered to the faithful.”
Even if you disagree about the merits of standing, obey. As it has at the end on n. 43: “With a view to a uniformity in gestures and postures during one and the same celebration, the faithful should follow the directions which the deacon, lay minister, or priest gives according to whatever is indicated in the Missal.”
Hopefully everyone else will as well, leading to: “42. … A common posture, to be observed by all participants, is a sign of the unity of the members of the Christian community gathered for the Sacred Liturgy: it both expresses and fosters the intention and spiritual attitude of the participants.”