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This paper proposes a method to improve the perceptual quality of an end-to-end neural speech coder using density models for bottleneck samples. Two parametric and non-parametric approaches are explored for modeling the bottleneck sample density. The first approach utilizes a sub-network to generate mean-scale hyperpriors for bottleneck samples, while the second approach models the bottleneck samples using a separate sub-network without any side information. The whole network, including the sub-network, is trained using PAM-based perceptual losses in different timescales to shape quantization noise below the masking threshold. The proposed method achieves a frame-dependent entropy model that enhances arithmetic coding efficiency while emphasizing perceptually relevant audio cues. Experimental results show that the proposed density model combined with PAM-based losses improves perceptual quality compared to conventional speech coders in both objective and subjective tests.