It was about 300 years from William Harvey's publication of his insights into the circulation of the blood before bloodletting fell out of common use. De Motu Cordis was published in 1628 - 'An Anatomical Exercise on the Motion of the Heart and Blood in Living Beings'. The last medical text recommending palliative bloodletting was published in the 1920's (iirc).
https://en.wikipedia.org/wiki/William_Harvey#De_Motu_Cordis / https://en.wikipedia.org/wiki/Exercitatio_Anatomica_de_Motu_...
I found a paper by some medical historians that said medicine became useful between 1910 and 1912: where a random person going to a random doctor with a random condition was more likely to be helped than harmed.