Virtual Bass Enhancement (VBE) refers to a class of digital signal processing algorithms that aim at enhancing the perception of low frequencies in audio applications. Such algorithms typically exploit well-known psychoacoustic effects and are particularly valuable for improving the performance of small-size transducers often found in consumer electronics. Though both time- and frequency-domain techniques have been proposed in the literature, none of them capitalizes on the latest achievements of deep learning as far as music processing is concerned. In this letter, we propose a novel time-domain VBE algorithm that incorporates a deep neural network for music demixing as part of the processing pipeline. This technique is shown to improve the bass perception and reduce inharmonic distortion, i.e., the main issue of existing time-domain VBE algorithms. The results of a perceptual test are then presented, showing that the proposed method is able to outperform state-of-the-art algorithms both in terms of bass enhancement and basic audio quality.