Density-based clustering focuses on defining clusters consisting of contiguous regions characterized by similar densities of points. Traditional approaches identify core points first, whereas more recent ones initially identify the cluster borders and then propagate cluster labels within the delimited regions. Both strategies encounter issues in presence of multi-density regions or when clusters are characterized by noisy borders. To overcome the above issues, we present a new clustering algorithm that relies on the concept of bridge point. A bridge point is a point whose neighborhood includes points of different clusters. The key idea is to use bridge points, rather than border points, to partition points into clusters. We have proved that a correct bridge point identification yields a cluster separation consistent with the expectation. To correctly identify bridge points in absence of a priori cluster information we leverage an established unsupervised outlier detection algorithm. Specifically, we empirically show that, in most cases, the detected outliers are actually a superset of the bridge point set. Therefore, to define clusters we spread cluster labels like a wildfire until an outlier, acting as a candidate bridge point, is reached. The proposed algorithm performs statistically better than state-of-the-art methods on a large set of benchmark datasets and is particularly robust to the presence of intra-cluster multiple densities and noisy borders.