Microbial interactions are expected to be major determinants of microbiome structure and function. Although fungi are found in diverse microbiomes, their interactions with bacteria remain largely uncharacterized. In this work, we characterize interactions in 16 different bacterial-fungal pairs, examining the impacts of 8 different fungi isolated from cheese rind microbiomes on 2 bacteria (Escherichia coli and a cheese-isolated Pseudomonas psychrophila). Using random barcode transposon-site sequencing with an analysis pipeline that allows statistical comparisons between different conditions, we observed that fungal partners caused widespread changes in the fitness of bacterial mutants compared to growth alone. We found that all fungal species modulated the availability of iron and biotin to bacterial species, which suggests that these may be conserved drivers of bacterial-fungal interactions. Species-specific interactions were also uncovered, a subset of which suggested fungal antibiotic production. Changes in both conserved and species-specific interactions resulted from the deletion of a global regulator of fungal specialized metabolite production. This work highlights the potential for broad impacts of fungi on bacterial species within microbiomes.