I was wondering if this is just a literal translation of the English phrase?
If the Wikipedia entry for "bed of roses" was correct in stating that this phrase was coined by the English dramatist Christopher Marlowe, I assume it would have had to originate from English. If I am reading between the lines of your question correctly, I do not believe Murakami would have been the first to do this translation due to the sheer frequency of the phrase (see my next answer). (See update below.)
would a typical native Japanese speaker know what it means, where it came from, etc.?
I cannot personally comment on this as a non-native speaker of Japanese. However, a search for the exact phrase in Google and for 薔薇{ばら}の寝床 yield a combined total of 281k results, suggesting to me that the phrase appears frequently enough for everyday use.
Update: The method used above to answer this question is completely unreliable! In reality, Google reports a combined total of only 145 hits for these two searches. Unless I learn of another way to estimate the frequency this phrase is used, I'm afraid I am unable to answer this question at my current level of Japanese.
Also, while I'm asking, is this something that Murakami does often? I've often read that Murakami writes "American Japanese" but I've never really understood what is meant by that.
My suspicion is that "American Japanese" may refer more to his style, rather than his use of specific words and phrases (though using phrases of foreign origin may serve this stylistic purpose).
For example, in a Publisher's Weekly interview, Murakami stated:
You have to know that the writing in Japan for Japanese people is in a particular style, very stiff. If you are a Japanese novelist you have to write that way. It's kind of a society, a small society, critics and writers, called high literature. But I am different in my style, with a very American atmosphere.
His description of Japanese literature as "very stiff" and written "in a particular style" suggests to me that he is trying to describe American literature (and his own writing) as, by contrast, more relaxed and less-constrained stylistically. Again, it is possible that the use of translated phrases like "bed of roses" serves this purpose, but to say "American Japanese" does seem to describe something larger than simply word choice.