Grading of the chain: This chain is "sahih". However, there is disagreement over al-Hasan al-Basri in it as to whether this narration is connected (mawsul) or mursal, and also over the name of the Companion; but such disagreement is not harmful, as will be explained below.

Reference / Source: Abu Dawud (4662) narrated it from Muhammad bin al-Muthanna, and al-Tirmidhi (3773) from Muhammad bin Bashshar; both of them narrate it from Muhammad bin 'Abdullah al-Ansari, with this chain. Imam al-Tirmidhi said: This hadith is "hasan sahih".

Reference and verification: Al-Nasa'i (10011) narrated it by way of Khalid bin al-Harith, from Ash'ath bin 'Abd al-Malik, from al-Hasan, from one of the Companions of the Prophet (peace and blessings be upon him) (i.e. Anas), and mentioned something similar.
Error and preponderance: In our view this is an error by Khalid bin al-Harith. More than one narrator narrated it from Khalid bin al-Harith in this way, with the name "Anas" (in place of Abu Bakrah). Yet the hadith is mahfuz (preserved) as that of "Abu Bakrah" (may Allah be pleased with him), as Muhammad bin 'Abdullah al-Ansari narrated it from Ash'ath bin 'Abd al-Malik, and as others besides Ash'ath also narrated it from al-Hasan.
General principle: In any case, disagreement of this kind is not harmful, because whichever Companion the hadith is narrated from, all the Companions are "'udul" (upright).

Reference / Sources: Ahmad (34/ 20392), al-Bukhari (2704, 3629, 3746, 7109) and al-Nasa'i (1730, 8110, 10010) narrated it by way of Abu Musa Isra'il bin Musa, and Ahmad (20448, 20516) and Ibn Hibban (6964) by way of al-Mubarak bin Fadalah. Both of them (Isra'il and al-Mubarak) narrate it from al-Hasan al-Basri, from Abu Bakrah.

Corroborations: A group corroborated them in narrating this report from al-Hasan al-Basri in "connected" form with mention of Abu Bakrah; Ibn 'Asakir mentioned their narrations in "Tarikh Dimashq" (13/ 231-238), and among them are Mansur bin Zadhan and Yunus bin 'Ubayd.

Reference / Mursal: Al-Nasa'i narrated it in (10012) by way of 'Awf al-A'rabi, in (10013) by way of Dawud bin Abi Hind, and in (10014) by way of Hisham bin Hassan; all three of them narrate it from al-Hasan al-Basri in "mursal" form. But since the connection (wasl) has been established from al-Hasan al-Basri through other routes, this irsal is not harmful.

Reference: This narration will also come below by way of 'Ali bin Zayd bin Jud'an from al-Hasan al-Basri in "connected" form, with mention of Abu Bakrah.