I asked Ayesha, "How did the Prophet ﷺ pray at night?"She replied, "He would sleep during the first part of the night and rise in the latter part to pray, then return to his bed. When the muadhin called the adhan, he would spring up. If he needed to bathe, he would do so, otherwise he would perform wudu and go out."
سألت عائشة، كيف صلاة النبي ﷺ بالليل؟ قالت: كان ينام أوله ويقوم آخره فيصلي، ثم يرجع إلى فراشه، فإذا أذن المؤذن وثب، فإن كانت به حاجة اغتسل، وإلا توضأ وخرج.
Bukhari reported it in the chapter on tahajjud (1146), and Muslim in the chapter on the prayer of travelers (739), both from the hadith of Abu Ishaq, from Aswad bin Yazid, and the wording is Bukhari's. The hadith contains further details mentioned in the book of wudu, in the chapter on the permissibility of a person in a state of major impurity sleeping without performing wudu.