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 is His slave and Messenger. We ask Allaah to exalt his mention as well as that of his family and all his companions.
There is no harm in keeping the Quran in the bedroom; it is like keeping it in any other rooms provided the place where the Quran is kept is pure. There is also no harm in changing clothes in the room where the Quran is kept as there is no evidence which prohibits this. Therefore, it is not an obligation to cover it when changing clothes. However, the Quran should not be kept open when not reading it as that exposes its chapters and verses to dust, as it is an obligation to protect it well and honour it.
Allaah Knows best.