differs with different points, and one must have a real reason to do this
some thoughts

position of patient:
example 1.
bleeding the yintang is fraught with things which go wrong
if patient is positioned head level with feet, blood, if profuse may run
into the eyes and create a hairy situation

example 2.
bleeding UB 40 post trauma, patient is better off standing to make the
requisites movements to set the prognosis

clotting time:
if one has nicked and the oozing has begun, and continues well beyond
clotting time, this is the wrong time to ask the patient if he or she is
a 'bleeder'

on blood liquefiers:
several conditions require intensive medication to prevent clotting, one
needs to clear this before using the lancet

hypo static tendency:
if patient standing sitting and with this tendency, the smallest nick
will set off a postural blackout

***
technique:
make sterile, run through a checklist, make sure patient knows what to
expect etc

a disposable knife could prove better than a spring released lancet, you
can grade the incising pressure

a point on a limb might bleed better if a tourniquet proximal to it
'raises' the vessel
if not a simple 'holding' of the area proximal can also accentuate the
vessel

approach with care:
on Shu points in the back, especially in a Heart Overwhelming Lung
pattern, the smallest nick on the most innocuous point can precipitate
fierce oozing

bleeding + cupping:
good for Cold, settled in, involuted points
bad for turgid, blood laden Heated points

it is possible for a suction cup to fill up with an alarming splash if
one has touched a point which was better left alone

***

bleeding an acu point Vs bleeding elsewhere
there as many more places to bleed which are not sitting on an acu
point; by and large these present a better choice

***

final thought
it is impossible to bleed an acu point without sharply stimulating it at
the same time
does one really want to do this?

hope this helps

Dr. Holmes Keikobad
http://www.acu-free.com