We are still speaking about the Adhkar of Salah.
Imam Muslim (may Allah bestow mercy on his soul) reported in his Sahih on the authority of `Abdullah ibn `Abbas (may Allah be pleased with them) that he said: "The Messenger of Allah (peace be upon him) drew aside the curtain (of his room) and (he saw) people in rows (performing Salah) behind Abu Bakr. And he said: Nothing remains of the glad tidings of Prophethood except good visions which a Muslim sees or someone sees a vision for him. And see that I have been forbidden to recite the Qur'an in the state of bowing and prostration. So, far as Ruku` is concerned, extol in it the Great and Glorious Lord, and while prostrating yourselves be earnest in supplication, for it is fitting that your supplications should be answered." [Sahih Muslim No. 974].
The Prophet (peace be upon him) explained in this Hadith special Adhkar for Ruku` and Sujud [bowing down and prostration] after the prohibition of reciting the Qur'an during Ruku` and Sujud because they are meant for humbleness, submission, and reverence. As for Ruku`, it is permissible for a Muslim to mention the glory of his Lord, and that He is the Great who has all attributes of greatness and glory such as power, dignity, the full power, wide knowledge, and the perfection of glory...etc. Moreover, a person says that no one deserves this greatness, glory, and praising except Allah, so it is incumbent on the people to glorify Him with their hearts, tongues, and actions.
Ibn Al Qayyim (may Allah bestow mercy on his soul) said: The best words a person says during Ruku` are "Subhan Rabbiya Al `Azhim [Glorified is my Lord, the Great]." Allah commanded His Servants to say that and revealed to the Prophet (peace be upon him) to instruct the people to say that Dhikr in this particular position. When Allah's Saying: "Then glorify with praises the Name of your Lord, the Most Great." [Surat Al Waqi`ah: 47] was revealed, the Messenger of Allah (peace be upon him) said: Say it in your Ruku`.
In general, the secret of Ruku` is the glorification of the Lord (Glory be to Him) with the heart and words, therefore the Messenger of Allah (peace be upon him) said: "Use it in your Ruku`." [The book of Salah, p. 176].
It is permissible for a Muslim to invoke Allah frequently during Ruku` because it will be answered, as it is the condition of drawing nearer to Allah and showing submission to Him. It was authentically reported in Sahih Muslim on the authority of Abu Hurayrah (may Allah be pleased with him) who narrated: The Prophet (peace be upon him) said: "A person becomes nearer to his Lord when he is in prostration. So, increase supplications while prostrating." It was reported in the previous Hadith that the Messenger of Allah (peace be upon him) said: "And exert yourself in supplication in prostration. Thus, your supplications are liable to be accepted" because a person is so near to his Lord during prostration, and the best condition for answering invocations is while prostration.