Ways to pray during exposition:
[137.] Exposition of the Most Holy Eucharist must always be carried out in accordance with the prescriptions of the liturgical books. [Cf. HCWEOM 82-100; GIRM 317; Code of Canon Law 941 § 2] Before the Most Holy Sacrament either reserved or exposed, the praying of the Rosary, which is admirable “in its simplicity and even its profundity”, is not to be excluded either. [Pope John Paul II, Apostolic Letter, Rosarium Virginis Mariae 2] Even so, especially if there is Exposition, the character of this kind of prayer as a contemplation of the mystery of the life of Christ the Redeemer and the Almighty Father’s design of salvation should be emphasized, especially by making use of readings taken from Sacred Scripture.[Cf. Congregation for Divine Worship and the Discipline of the Sacraments, Letter of the Congregation, 15 January 1997: Notitiae 34 (1998) pp. 506-510; Apostolic Penitentiary, Letter to a Priest, 8 March 1996: Notitiae 34 (1998) p. 511]
I don’t think the Bible has entered into the thinking of people who attend exposition of the Sacrament, though it probably happens more often today than, say, fifty years ago.
Liturgy of the Hours is also a thought.
Most people are on board with this:
[138.] Still, the Most Holy Sacrament, when exposed, must never be left unattended even for the briefest space of time. It should therefore be arranged that at least some of the faithful always be present at fixed times, even if they take alternating turns.
I remember a curious episode in my rural parish over a decade ago. Since we did not have a resident priest, and as a lay person, I am not empowered to give a “blessing” of any sort, I went for the final half-hour of exposition, and there was one parishioner remaining. I figured I would repose the sacrament when she was done praying. But we went about a half-hour past the scheduled conclusion. Finally, either she left or I reposed the Sacrament. I asked her about it a few days later, and she said she was resolved to stay as long as the Sacrament was on display–and why didn’t I repose sooner? I laughed to myself and mused that I didn’t really count as one of the faithful …