Praise be to Allah.
There is nothing wrong with a man or woman praying in the bedroom, because the Prophet (peace and blessings of Allaah be upon him) said: “The earth has been made a place of prostration and a means of purification for me, so wherever a man of my ummah is when the time for prayer comes, let him pray.” Narrated by al-Bukhaari (335) and Muslim (521).
The Prophet (peace and blessings of Allaah be upon him) used to offer naafil prayers and qiyaam al-layl in the room of ‘Aa’ishah (may Allaah be pleased with her) and the rooms of his other wives (may Allaah be pleased with them).
It is well known that men are enjoined to offer prayer in congregation, when the call for prayer is given, but if a man misses a prayer or is excused for not going to the mosque, or he offers a naafil prayer in his bedroom, there is nothing wrong with that. But if he misses prayer in congregation in the mosque with no excuse, and prays in his room, his prayer is valid but he is sinning by not praying in congregation.
The point is that there is no difference between a bedroom and any other place in the house that is taahir (pure).
And Allaah knows best.