well are you going to listen to the Qura'an through the headphones *in* a bathroom?
If you're sitting in a dirty *bus* for instance..and you have your headphones on..then you're good..even the *seemingly* clean places might have dirt in them...the distinction in the matter you mentioned has to do with *najasa* or *impurity*..where there is *impurities* you refrain from mentioning the name of Allah (swt)..recite the Qura'an..read it..or so on..obviously..a bathroom is a place which contains *najasa*..so nothing *holy* or *taahir* (pure) should enter it..
EXCEPT..in one little situation..when you go into a bathroom..specifically when you step in...and this is according to a hadith by Rasulullah (saaws)...one should say *allahoma inni ao'otho bika minal khobthi wal khabaae'eth* (Ya Allah I seek refuge with you from al-kobthi and al-khabaae'eth)
Al-Khobthi..are male jinns..Al-Khabaae'eth..are female jinns..and the reason why you say what is quoted above is to first have a veil casted over their eyes so they do not see you in the bathroom..and then to protect you from their evils
That's the only time you get a free pass for this (so to speak)..mind you..one should still be careful about this matter..especially in the West where bathrooms are set up different (in many Muslim countries the bathroom *altogether* is not even *put* anywhere close to the *qibla*..and it's just the *direction* of prayer..normally things are architecturalized so it's built in a neutral spot..so imagine!)
and Allah Knows Best
