Praise be to Allah.
Undoubtedly this action is bid’ah, because it has not been transmitted to us that the Prophet (peace and blessings of Allaah be upon him) or his companions did that, and all goodness is to be found in following them. But if a person says Tasbeeh to himself, there is nothing wrong with that, indeed it brings much good and a great reward, because it was narrated in a saheeh report that the Prophet (peace and blessings of Allaah be upon him) said: “The most beloved of words to Allaah are four: Subhaan Allaah (Glory be to Allaah), al-hamdu Lillaah (praise be to Allaah). Laa ilaaha ill-Allaah (there is no god except Allaah) and Allaahu akbar (Allaah is Most Great).” (Narrated by Muslim, al-Adaab, 2137)
And he (peace and blessings of Allaah be upon him) said: “Two words which are light on the tongue but which are dear to the Most Merciful and will weigh heavily in the balance: Subhaan Allaah wa bi hamdih, subhaan Allaah il-‘Azeem (Glory and praise be to Allaah; Glory be to Allaah the Almighty).” (Narrated by al-Bukhaari, al-Aymaan wa’l-Nudhoor, 6682; Muslim, al-Dhikr wa’l-Du’a’ wa’l-Tawbah (Remembering Allaah, supplication and repentance, 2694).