Clustering partitions a collection of objects into groups called clusters, such that similar objects fall into the same group. Similarity between objects is defined by a distance function satisfying the triangle inequality; this distance function along with the collection of objects describes a distance space. In a distance space, the only operation possible on data objects is the computation of distance between them. All scalable algorithms in the literature assume a special type of distance space, namely a k-dimensional vector space, which allows vector operations on objects. We present two scalable algorithms designed for clustering very large datasets in distance spaces. Our first algorithm BUBBLE is, to our knowledge, the first scalable clustering algorithm for data in a distance space. Our second algorithm BUBBLE-FM improves upon BUBBLE by reducing the number of calls to the distance function, which may be computationally very expensive. Both algorithms make only a single scan over the database while producing high clustering quality. In a detailed experimental evaluation, we study both algorithms in terms of scalability and quality of clustering. We also show results of applying the algorithms to a real-life dataset.