Traffic state estimation is a challenging task due to the collection of sparse and noisy measurements from specific points of the traffic network. The emergence of Connected and Automated Vehicles (CAVs) provides new capabilities for traffic state estimation using extended floating car data such as position, speed and spacing information. In this work we propose a Bayesian Traffic State Estimation (BTSE) methodology for estimating the traffic density based on extended floating car data. BTSE utilizes the Bayesian paradigm to express any prior information to derive probability distributions of the traffic density of different road segments of the traffic network. Two variations of the BTSE methodology are developed to handle the offline and online estimation problem. The BTSE methodology is evaluated both using realistic SUMO microsimulations for M25 Highway, London, U.K., and a real-life vehicle-trajectory dataset from German highways, extracted from videos recorded by drones. The efficiency and accuracy of the BTSE methodology is compared to an existing methodology in the literature. We present results for the estimation performance of the methods showing that the Bayesian methodology consistently results in lower mean absolute percentage error than the compared literature method. The BTSE methodology yields high-quality estimation results even for a low penetration rate of CAVs (e.g. 5%).