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We propose a novel neural waveform compression method to catalyze emerging speech semantic communications. By introducing nonlinear transform and variational modeling, we effectively capture the dependencies within speech frames and estimate the probabilistic distribution of the speech feature more accurately, giving rise to better compression performance. In particular, the speech signals are analyzed and synthesized by a pair of nonlinear transforms, yielding latent features. An entropy model with hyperprior is built to capture the probabilistic distribution of latent features, followed with quantization and entropy coding. The proposed waveform codec can be optimized flexibly towards arbitrary rate, and the other appealing feature is that it can be easily optimized for any differentiable loss function, including perceptual loss used in semantic communications. To further improve the fidelity, we incorporate residual coding to mitigate the degradation arising from quantization distortion at the latent space. Results indicate that achieving the same performance, the proposed method saves up to 27% coding rate than widely used adaptive multi-rate wideband (AMR-WB) codec as well as emerging neural waveform coding methods.