In trauma and critical care settings, rapid and precise intravascular access is key to patients' survival. Our research aims at ensuring this access, even when skilled medical personnel are not readily available. Vessel bifurcations are anatomical landmarks that can guide the safe placement of catheters or needles during medical procedures. Although ultrasound is advantageous in navigating anatomical landmarks in emergency scenarios due to its portability and safety, to our knowledge no existing algorithm can autonomously extract vessel bifurcations using ultrasound images. This is primarily due to the limited availability of ground truth data, in particular, data from live subjects, needed for training and validating reliable models. Researchers often resort to using data from anatomical phantoms or simulations. We introduce BIFURC, Bifurcation Identification for Ultrasound-driven Robot Cannulation, a novel algorithm that identifies vessel bifurcations and provides optimal needle insertion sites for an autonomous robotic cannulation system. BIFURC integrates expert knowledge with deep learning techniques to efficiently detect vessel bifurcations within the femoral region and can be trained on a limited amount of in-vivo data. We evaluated our algorithm using a medical phantom as well as real-world experiments involving live pigs. In all cases, BIFURC consistently identified bifurcation points and needle insertion locations in alignment with those identified by expert clinicians.