In a recent Q&A post, a reader and I talked in the comments about the proper rubrics or gestures to be used while praying the hours: when to stand, when to sit, signs of the cross, etc.
Although the sitting vs. standing is of more importance during a group recitation of the Divine Office, especially when done in a church or other public setting (as opposed to in private and/or at home), there are some gestures which are easy to do in any situation, and they are helpful to our sense of reverence and devotion.
Traditionally, anytime the Blessed Trinity is named,we should bow. (Either at the waist or at the head.)
This happens every time we say the doxology (Glory Be), both after each psalm and at the opening verse, following, O God, come to my assistance.
In addition, many hymns have a final verse that references the Trinity. For example, at the end of "On This Day, the First of Days" we have,
God the blessed Three in One,
May thy Holy will be done,
In thy word our souls are free
And we rest this day with thee.
Another example is "Creator of the Stars of Night":
To God the Father, God the Son,
And God the Spirit, Three in One,
Praise, honor, might, and glory be
From age to age eternally.
A bow at the beginning of such a trinitarian hymn verse would be appropriate.
It makes sense. The Trinity is the central mystery of our faith. To state the Name and the nature of God calls for a gesture of reverence. The greatness of the Trinity is reinforced in our minds when we pray not just with our lips, but by engaging another part of the body.
That is the point, in fact, of all liturgical gestures and postures--to engage not just the mind in prayer, but our senses, muscles, bones. All of me. Every bodily member, straining eagerly to offer praise and adoration.