Ruling on praying on one’s bed

Yes, it is permissible to
pray on one’s bed so long as it is firm and the worshipper is able to place
his forehead and nose firmly when prostrating. 

Among the comments made by
scholars about praying on one’s bed are the following: 

1 – al-Hattaab said in
Mawaahib al-Jaleel (1/520): It says in al-Tawdeeh: As for praying
on one’s bed, there is no dispute that it is permissible, as is stated in
al-Bayaan. End quote. 

2 – al-Nawawi (may Allaah
have mercy on him) said in al-Majmoo’ (3/221): The condition for
obligatory prayer is that the worshipper be steady in facing the qiblah
throughout the prayer. If he faces the qiblah and does all the pillars
(essential parts) of prayer in a howdah or on a bed or the like on the back
of a riding-animal that is standing, there are two views as to whether his
obligatory prayer is valid; the more correct view is that it is valid, and
this was stated by the majority, because that is like praying on board a
ship. End quote. 

3 – Shaykh Saalih
al-Fawzaan (may Allaah preserve him) was asked: Is it permissible to pray in
a raised place such as on a bed and the like if one is not sure whether the
ground is clean and he has no excuse such as sickness and the like? 

He replied: There is
nothing wrong with praying on something that is raised such as a bed and the
like, if it is clean and is firm and will not shake or wobble and distract
the worshipper. End quote from al-Muntaqa (2/143). 

And Allaah knows best.