Sounds like it may be "Molluscum Contagiosa".  No pain, small white
bump that looks like a pimple or ingrown hair but can't be popped, and
the bleeding.  Usually turns a reddish color and has a concave
impression in the center of the bump?  It's actually a wart like
growth, with a core hence the bleeding, that will go away on its own
or they can be removed by a doctor.

I've seen a few posts on here with people remarking on these types of
symptoms.  I wonder if molluscum is becoming more widespread?

I still read posts on here and I feel lucky to walk away with just
molluscum.  BUT, I'm thoroughly freaked about sex now and even the
slightest abnormality on my lip or genital area scares the hell out of
me nowadays.  Who knows what I'll break-out with in the future.  I'm
not even all that sexually active at the moment but still feel I'll
get something else someday.  There are some VERY kind, understanding,
empathizing souls who post here.  This forum is such a great outlet
for those with inquiring minds and symptoms of something out of the
ordinary.

However the one think I've learned or walked away with from reading
this site and seriously boning-up (pardon the pun) on STD's is the
fact doctors, medical practitioners, medical minds in general don't
have the slightest clue about any of these F***ing viruses.  They lie
dormant for years, people have it but don't show symptoms, money
making "viral inhibitors", oral to genital transmission, hsv, hpv,
false positive and negative testing, epstein-barr to shingles to
chicken pox...BLAH!  Sounds like any sexually active adult is probably
a carrier of something and there won't be a cure for any virus until
the year 2200, at the earliest.  Just hope your body has a strong
immune system is about all one can do, or maybe enter a monastery or
convent (but then you might get shingles or molluscum by sharing a
towel or toilet).  My heart goes out to those stricken with the
grandaddy of all the wretched viruses, AIDS...bless you all.

Sam