My head has no face,
but I breathe and bleed.
I am quiet,
but my visitors love to sing.
Who or what am I?
I'll throw my hat into the ring. The first line is a stretch, but the others fit well.
A Tree
My head has no face,
Trees are sometimes compared to old men (Old Man Willow), but do not have human faces.
but I breathe and bleed.
Plants can 'breath' using processes such as photosynthesis and respiration. Trees bleed sap.
I am quiet,
Trees don't make noise on their own.
but my visitors love to sing.
Birds nest in trees, and many love to sing.
......
My guess (yes, I love answering your riddles...)
Microphone
My head has no face:
The top of the microphone is considered the head.
but I breathe and bleed.
There's a such thing as microphone bleed, and I'm guessing the mesh is the 'breathe' part.
I am quiet:
Microphones by themselves don't make noise
but my visitors love to sing.
Microphones are used generally for singing (karaoke, anyone?)
Even if it's not the right answer, it makes sense to me (I'm a musician by hobby).
I was convinced it was
a shower
My head has no face,
obviously a shower head has no face
but I breathe and bleed.
all showers dispense water (bleed) and some have additional hot air jets (breathe)
I am quiet, but my visitors love to sing.
who doesn't sing in the shower?
I was thinking it might be
"a glass of beer."
Beer's foam is commonly called a "head."
Beer breathes and bleeds - it "breathes" because of the bubbles, and "bleeds" when someone takes a sip.
Beer itself is quiet, but in a pub, where there's lots of drinking, there might be singing.
That's my take - good riddle!