She had lost a lot of blood and doctors decided to do a transfusion (A. to B. on) her. Should I choose A or B? Thanks l lot.
Neither. They decided to "give her a transfusion". If this is a question from a grammar book exercise, it's another example of a sentence that doesn't sound natural in English.
If they absolutely insists on one of those answers, then it would have to be "on" because we wouldn't "do a transfusion to someone" or "do a/n [anything] to someone". In medical terms, we might rarely say something like "they did an operation on her" though again the majority of people would use "they operated on her".