Amr bin Dinar عمرو بن دينار الأثرم الجمحي · The Book of Purification and its Sunnah

"I came to the Prophet when he was performing ablution and greeted him with the Salam, but he did not return (the greeting). When he had finished his ablution he said: 'Nothing prevented me from returning your greeting but the fact that I need to have ablution.'" (Da'if) Another chain with similar wording.

When it was the year of the Conquest (of Makkah), the Messenger of Allah got up to perform a bath and Fatimah screened him. Then he took his garment and wrapped himself in it (such that it became like the towel used to dry oneself).