This has bee n narrated though a different chain of narrators by 'Aishah. This version has the words:

"She used to take a bath for every prayer." Abu Dawud said: Al-Qasim b. Mabrur reported from Yunus from Ibn Shihab from 'Amrah from 'Aishah from Umm Habibah daughter of Jahsh. Similarly, it was reported by Ma'mar from al-Zuhri from 'Amrah from 'Aishah. Ma'mar sometimes reported from 'Amrah on the authority of Umm Habibah to the same effect. Similarly, it was reported by Ibrahim b. Sa'd and Ibn 'Uyainah from al-Zuhri from 'Amrah from 'Aishah. Ibn 'Uyainah said in his version: He (al-Zuhri) did not say that the Prophet (ﷺ) commanded her to take bath. It has also been transmitted by al-Awza'i in a similar way. In this version he said: 'Aishah said: She used to take bath for very prayer.

حَدَّثَنَا يَزِيدُ بْنُ خَالِدِ بْنِ عَبْدِ اللَّهِ بْنِ مَوْهَبٍ الْهَمْدَانِيُّ، حَدَّثَنِي اللَّيْثُ بْنُ سَعْدٍ، عَنِ ابْنِ شِهَابٍ، عَنْ عُرْوَةَ، عَنْ عَائِشَةَ، بِهَذَا الْحَدِيثِ قَالَ فِيهِ فَكَانَتْ تَغْتَسِلُ لِكُلِّ صَلاَةٍ ‏.‏ قَالَ أَبُو دَاوُدَ رَوَاهُ الْقَاسِمُ بْنُ مَبْرُورٍ عَنْ يُونُسَ عَنِ ابْنِ شِهَابٍ عَنْ عَمْرَةَ عَنْ عَائِشَةَ عَنْ أُمِّ حَبِيبَةَ بِنْتِ جَحْشٍ وَكَذَلِكَ رَوَاهُ مَعْمَرٌ عَنِ الزُّهْرِيِّ عَنْ عَمْرَةَ عَنْ عَائِشَةَ وَرُبَّمَا قَالَ مَعْمَرٌ عَنْ عَمْرَةَ عَنْ أُمِّ حَبِيبَةَ بِمَعْنَاهُ وَكَذَلِكَ رَوَاهُ إِبْرَاهِيمُ بْنُ سَعْدٍ وَابْنُ عُيَيْنَةَ عَنِ الزُّهْرِيِّ عَنْ عَمْرَةَ عَنْ عَائِشَةَ وَقَالَ ابْنُ عُيَيْنَةَ فِي حَدِيثِهِ وَلَمْ يَقُلْ إِنَّ النَّبِيَّ صلى الله عليه وسلم أَمَرَهَا أَنْ تَغْتَسِلَ ‏.‏ وَكَذَلِكَ رَوَاهُ الأَوْزَاعِيُّ أَيْضًا قَالَ فِيهِ قَالَتْ عَائِشَةُ فَكَانَتْ تَغْتَسِلُ لِكُلِّ صَلاَةٍ ‏.‏