Many methods for 3D reconstruction of deformable surfaces from a monocular view relay on inextensibility constraints. An interesting application with commercial potential lies in augmented reality in portable and wearable devices. Such applications add an additional challenge to the 3D reconstruction, since in portable platforms the availability of resources is limited and not always guaranteed. Towards this goal, we introduce a method to deliver the best possible 3D reconstruction of the deformable surface at any time. Since computational resources may vary, it is decided on-the-fly when to stop the reconstruction algorithm. We use an efficient optimization method to quickly deliver the reconstructed surface. We introduce bootstrapping to improve the robustness of the efficient 3D reconstruction algorithm by merging multiple versions of the reconstructed surface. Also, these multiple 3D surfaces can be used to estimate the confidence of the reconstruction. In a series of experiments, in both synthetic and real data, we show that our method is effective for timely reconstruction of 3D surfaces.