<<The bed is swimming>> is grammatically correct present tense, but it makes no sense, as beds do not swim. People swim, fish swim, but beds dont swim!
Swimming could be used like an adjective as in: <<The bed was swimming in books and papers.>> This would mean that the bed was covered in books and papers. But for this usage to work, you must say what the bed is swimming in. (ie, books and papers)
The way you have it written, leaves too much of your idea to the readers imagination. A person cant be sure what you mean, and they might guess and be wrong!
Also, <<The bed is swam>> is wrong past tense. It should be <<The bed swam.>>, but again, that does not make any sense because beds don't swim!
You also said,
<<I just need to know what do you think when you read this statement :All night I make my bed swim>>
To me, it sounds like all night you make your bed wet!
But beds dont swim! So we must guess what it means, and it will mean different things to different people who are just guessing!
Hope this helps!
-LisaBObeesa