The Prophet ﷺ actually practiced this: he would frequently say in his bowing—and likewise in his prostration—“Subḥānaka Allāhumma rabbānā wa biḥamdik, Allāhumma ighfir lī” (Glory be to You, O Allah, our Lord; to You belongs all praise. O Allah, forgive me). The sense of this formula is that you exalt Allah—affirming the perfection of His attributes, denying every imperfection—and then beg His forgiveness.
Her second report adds that the Prophet ﷺ used to say while bowing and prostrating, “Subbūḥ quddūs, Rabb al-malāʾikah wa-r-rūḥ” (Supremely Glorified, Most Holy, Lord of the angels and the Spirit). The words subbūḥ quddūs are an emphatic declaration of His transcendence. Thus, exalted is He: Supremely Glorified, Most Holy, Lord of the angels—those unseen hosts who are Allah’s soldiers—and “the Spirit” here is Gabriel, the noblest of the angels. A worshipper should therefore abound in saying during his bowing and prostration, “Subḥānaka Allāhumma rabbānā wa biḥamdik, Allāhumma ighfir lī,” following the practice of the Messenger of Allah ﷺ, and should likewise say, “Subbūḥ quddūs, Rabb al-malāʾikah wa-r-rūḥ.”
As for the report of Ibn ʿAbbās (may Allah be pleased with them both), he said: “In bowing, glorify the Lord; in prostration, strive in supplication.” This is part of a longer hadith that begins: “Indeed I have been forbidden to recite the Quran while bowing or prostrating. Therefore, in bowing, glorify the Lord, and in prostration, exert yourselves in supplication, for it is most likely that you will be answered.” The phrase “most likely” (qamin) means that the response is expected, because the servant is never closer to his Lord than when he is in prostration. Accordingly, it is not permissible for anyone to recite the Quran while bowing or prostrating, yet he may make supplications drawn from the Quran itself—such as saying, for example, “Our Lord, forgive us our sins and our excess in our affairs, make firm our feet, and grant us victory over the disbelieving people” (Quran 3:147).