Neural implicit surfaces with signed distance functions (SDFs) achieve superior quality in 3D geometry reconstruction. However, training SDFs is time-consuming because it requires a great number of samples to calculate accurate weight distributions and a considerable amount of samples sampled from the distribution for integrating the rendering results. Some existing sampling strategies focus on this problem. During the training, they assume a spatially-consistent convergence speed of kernel size, thus still suffering from low convergence or errors. Instead, we introduce an error-aware sampling method based on thin intervals of valid weight distributions, dubbed adaptive shells, to reduce the number of samples while still maintaining the reconstruction accuracy. To this end, we first extend Laplace-based neural implicit surfaces with learned spatially-varying kernel sizes which indicates the range of valid weight distributions. Then, the adaptive shell for each ray is determined by an efficient double-clipping strategy with spatially-varying SDF values and kernel sizes, fitting larger kernel sizes to wider shells. Finally, we calculate the error-bounded cumulative distribution functions (CDFs) of shells to conduct efficient importance sampling, achieving low-variance rendering with fewer calculations. Extensive results in various scenes demonstrate the superiority of our sampling technique, including significantly reducing sample counts and training time, even improving the reconstruction quality. The code is available at https://github.com/erernan/ESampling.