Insight to the spatial and temporal scales of coevolution is key to predicting the outcome of host-parasite interactions and spread of disease. For bacteria infecting long-lived hosts, selection to overcome host defences is just one factor shaping the course of evolution; populations will also be competing with other microbial species and will themselves be facing infection by bacteriophage viruses. Here, we examine the temporal and spatial patterns of bacterial adaptation against natural phage populations from within leaves of horse chestnut trees. Using a time-shift experiment with both sympatric and allopatric phages from either contemporary or earlier points in the season, we demonstrate that bacterial resistance is higher against phages from the past, regardless of spatial sympatry or how much earlier in the season phages were collected. Similarly, we show that future bacterial hosts are more resistant to both sympatric and allopatric phages than contemporary bacterial hosts. Together, our results suggest the evolution of relatively general bacterial resistance against phages in nature and are contrasting to previously observed patterns of phage adaptation to bacteria from the same tree hosts over the same time frame, indicating a potential asymmetry in coevolutionary dynamics.