Morphable models are a backbone for many human-centric workflows as they provide a simple yet expressive shape space. Creating such morphable models, however, is both tedious and expensive. The main challenge is to carefully establish dense correspondences among raw scans that capture sufficient shape variation. This is often addressed using a mix of non-rigid registration and significant manual intervention. We observe that creating a shape space and solving for dense correspondence are tightly coupled – while dense correspondence is needed to build shape spaces, an expressive shape space can provide a reduced dimensional space to regularize the search. We introduce BLiSS, a method to solve both progressively. Starting from a small set of manually registered scans to bootstrap the process, we simultaneously enrich the shape space and then use that to automatically get new unregistered scans into correspondence. The critical component of BLiSS is a non-linear deformation model that captures details missed by the low-dimensional shape space, thus allowing progressive enrichment of the space. We show that ours produces, in the context of body variations, a shape space that is at par with state-of-the-art shape spaces (e.g., SMPL, STAR, GHUM), while requiring much fewer (e.g., 5%) manual registrations