What happens if my girlfriend is taking anticonceptive pills and her new menstrual cycle starts before she finishes the 28 pills in the blister?

Normal !: It takes a woman's body a few cycles to get used to the new hormones in the birth control pill. Most women will start to menstruate shortly after stopping the hormone pills while they are taking the placebos. The number of placebo pills can differ from one brand of birth control pill to another. If her bleeding is predictable, that's a good thing ! some women stop bleeding completely on the pill !

Need different pill: There are 20 different kinds of birth control pills. The difference basically is the ratio of estrogen to progesterone. Some pills have 90/10, some 80/20, some 70/30, some 50/50.. If she is have anticipatory bleeding before her expected period, then her pill needs to have a higher estrogen concentration to support the uterine lining. Talk to your fp and start a different birth control pill.