Note how her reaction to the blood bag is IDENTICAL IN PRETTY MUCH EVERY WAY, SHAPE AND FORM to Elena’s reaction to drinking from a blood bag for the first time. Yeah. Also, note how she then drank from the rest of the bag. (Which Elena didn’t (a) attempt, and (b) Caroline hadn’t just thrown up massive amounts of vampire blood). Yet, despite that full blood bag she consumed, the next time we saw her when Matt came to visit, she still looked pale, still had circles under her eyes. She still looked essentially like Elena did without drinking any human blood, thus completing her transition.
So still looking like hell warmed over, and despite drinking that full blood bag when the nurse came in and Caroline went all fang-y, she looked at that nurse, smelt her fresh, lovely human blood and proclaimed: “I’m STARVING!” then went for the jugular (literally). Yuppers, it was only until Caroline had drunk from a human directly from the vein that she fully transitioned and was the picture of perfect health. Just like Elena. After drinking from Matt and fully transitioning, Elena hadn’t tried blood bags, or animal blood. So for all we know, and based on what we saw with Caroline, Elena would have been able to pick up and drink from a blood bag at any point after she drank from Matt and transitioned.