When does charitable work become an organized act, and when does it become an innovation (bid'ah)? How can one distinguish between the two, and are there any useful references on this matter?

The default rule concerning good deeds is that they are permissible, not innovations (bid‘ah). Allah Almighty commanded the performance of good deeds when He said: "And do good that you may succeed." He also commanded hastening to good deeds. Organizing charitable works and institutions is not considered an innovation. One may ask firmly grounded scholars about what might be unclear regarding this matter. Among the works that generally discuss innovations and differentiate them from the Sunnah are: Al-I’tisam by Al-Shatibi, and Al-Ibda’ fi Madarr al-Ibtida’ by Dr. Ali Mahfouz.