I use bulb syringes when nasal secretions are interfering with a newborn's
comfort and ability to feed. I am not in the delivery room, but with mothers
and babies after recovery and during the first few days. Occasionally, IMHO,
they are needed.
There are two sizes that I use: One, the small, baby blue type, useful for
small babies or small noses. The other is the turquoise one that is larger,
useful for more average sized babies. They should be used carefully and
quickly, because it can frighten babies.
Where I work right now, there is only the small size syringe...it goes too far
in larger noses, and irritates, or pokes into the tender nasal passageway
tissue, and both hurts and  doesn't quickly remove the foreign matter. The
nurses are afraid of the large ones, and think they(the large syringes)
contribute to problems. I think the right sized one used carefully(and only
when needed) can help a baby breathe or eat.
I explain it to parents  a bit like Miriam does, saying that they may never
need to use it, but when a baby has a "cold" and can't breathe easily, they
are irritable, and don't sleep well, and don't breastfeed well. It's like if
we went to sleep with a real runny nose...we would blow our nose with a
tissue. Baby can't do that, but we can help them. No, they didn't have bulb
syringes in days of old, but mothers resorted to sucking out the mucus with
their mouths. Obviously it was done only when really needed, but that's how
it's done. Mothers still do it, having worked at a big city clinic with many
different cultural groups.
I'd like to see a study on the use of bulb syringes, but it seems hard to
design with such variation in the skill of the user, and what determines a
need. Delivery room bulb syringe use I would also like to see studied, to make
sure we are not doing more harm than good(now that's an idea!) with something
that "we've always used".

Happy New Year All!
Fritzi Drosten, RN, IBCLC
Piedmont, California