Yes, there's a high probability that even after a thorough wash cycle, DNA will still be detectable.
Leaving aside the thoroughness of the wash, at the end of the day, it depends on the method of DNA analysis that would be used. The older methods would be virtually useless in these circumstances, but there would be a good chance that the various PCR techniques would work.
However, there is now a method based upon the PCR system called Polymerase Chain Reaction of Short Tandem Repeats which would almost certainly detect the presence of DNA after laundering.
Polymerase Chain Reaction of Short Tandem Repeats was developed in the USA and has been tested in the courts over there numerous times in cases of indecent assault and other unsavoury matters not suitable for discussing here. Courts in the USA and other countries are now accepting the infallibility of the method, resulting in the conviction of the accused with hardly any exceptions.
In my university biochemistry department, we've got three state-of-the-art DNA analysers that employ this very method. Having seen their sensitivity at first hand myself, rest assured, I'm fairly confident we'd find your DNA whether the bedclothes had been laundered or not.
Incidentally, not all Forensic Science laboratories have such sophisticated equipment, so there's a chance you might get away with it, whatever "it" may be.