Single-pixel imaging has emerged as a key technique in fluorescence microscopy, where fast acquisition and reconstruction are crucial. In this context, images are reconstructed from linearly compressed measurements. In practice, total variation minimisation is still used to reconstruct the image from noisy measurements of the inner product between orthogonal sampling pattern vectors and the original image data. However, data can be leveraged to learn the measurement vectors and the reconstruction process, thereby enhancing compression, reconstruction quality, and speed. We train an autoencoder through self-supervision to learn an encoder (or measurement matrix) and a decoder. We then test it on physically acquired multispectral and intensity data. During acquisition, the learned encoder becomes part of the physical device. Our approach can enhance single-pixel imaging in fluorescence microscopy by reducing reconstruction time by two orders of magnitude, achieving superior image quality, and enabling multispectral reconstructions. Ultimately, learned single-pixel fluorescence microscopy could advance diagnosis and biological research, providing multispectral imaging at a fraction of the cost.