The best piece of evidence from the text that supports the researchers' claim of a relationship between bumblebee infections and their proximity to honeybee apiaries is:
the percentage of bumblebees infected based on their proximity to apiaries.
This is specifically supported by the information that indicates a higher percentage of bumblebees close to apiaries carried the deformed wing virus, while none of the bumblebees tested more than a half mile away from the apiaries showed any signs of the virus. This direct correlation highlights the influence of proximity to honeybee colonies on bumblebee virus infections.