All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His Slave and Messenger.
It is permissible to recite the Quran or read Hadeeth books and scholars’ Fataawa while lying in one's bed; ‘Aa’ishah said: “The Messenger of Allaah, sallallaahu ‘alayhi wa sallam, would rest on my lap when I was menstruating and recite the Quran.” [Muslim]
An-Nawawi said: “It implies that it is permissible to recite the Quran while lying down and while resting on a menstruating woman.”
Allaah Knows best.