Bat species worldwide are receiving increased attention for the discovery of emerging viruses, cross-species transmission, and zoonoses, as well as for characterizing virus infections specific to bats. In a previous study, we investigated the presence of coronaviruses in faecal samples from bats at different locations in Denmark, and made phylogenies based on short, partial ORF1b sequences. In this study, selected samples containing bat coronaviruses from three different bat species were analysed, using a non-targeted approach of next-generation sequencing. From the resulting metagenomics data, we assembled full-genome sequences of seven distinct alphacoronaviruses, three astroviruses, and a polyomavirus, as well as partial genome sequences of rotavirus H and caliciviruses, from the different bat species. Comparisons to published sequences indicate that the bat alphacoronaviruses belong to three different subgenera—i.e., Pedacovirus, Nyctacovirus, and Myotacovirus—that the astroviruses may be new species in the genus Mamastrovirus, and that the polyomavirus could also be a new species, but unassigned to a genus. Furthermore, several viruses of invertebrates—including two Rhopalosiphum padi (aphid) viruses and a Kadipiro virus—present in the faecal material were assembled. Interestingly, this is the first detection in Europe of a Kadipiro virus.