In early 2024, an unprecedented outbreak of H5N1 high pathogenicity avian influenza was detected in dairy cattle in the USA. The epidemic remains uncontrolled, with spillbacks into poultry, wild birds and other mammals including humans. Here, we present molecular and virological evidence that the cattle B3.13 genotype H5N1 viruses rapidly accumulated adaptations in polymerase genes that enabled better replication in bovine cells, as well as cells of other mammalian species including humans and pigs. We find evidence of several mammalian adaptations gained early in the evolution of these viruses in cattle including PB2 M631L, which is found in all cattle sequences, and PA K497R, which is found in the majority. Structurally, PB2 M631L maps to the polymerase-ANP32 interface, an essential host factor for viral genome replication. We show this mutation adapts the virus to co-opt bovine ANP32 proteins and thereby enhances virus replication in bovine and primary human airway cells. Importantly, we show that ongoing evolution during 2024 in the PB2 gene, including a convergently arising D740N substitution, further increases polymerase activity in a range of mammalian cells. Thus, the continued circulation of H5N1 in dairy cattle allows virus adaption improving replicative ability in cattle and increasing zoonotic spillover risk.