I am a 70 year old female. One of my nipples has inverted very recently.

Thank you for sharing your question.  Because of the acute change I would definitely urge you to see your ob/gyn for an in-person examination.  This inversion needs to be worked up further with an in-person examination and a new set of mammograms.  Best wishes.

. . . especially if associated with any (bloody) drainage.  A new unilateral inversion in anyone over 40 needs to have a formal breast exam and possible work-up (mammogram, etc.) with an oncologic breast surgeon, to rule out any new developments (especially with any family history of breast cancer). Not meant to alarm you, but early intervention always wise.

You should call a breast surgeon and be examined.  It will most likely be recommended that you have a mammogram.  Please don't wait too long.