Disk diffusion assay is based on, diffusion through the agar, and diffusion of large molecules is slow. So I would not recommend that assay.
How about placing different volumes of your nanoparticles in 96-well plate wells, supplement with water or buffer to constant volume, and adding your bacteria in X2 growth media? Do repeats and test for growth by turbidity. If you have a plate-reader capable of temperature control and shaking you can follow growth as OD change vs time (make sure to do your no-bacteria controls).
It difficult to determine the concentration absorbed by the disk as some solute may not penetrate, since the edges of the disks can serve as filters. To get accurate drugs in disks, the disks are impregnated with certain quantity to diffuse into the media. That begat why it is reported as disk CONTENT instead of CONCENTRATION.
I will advise that you use other type of assay like agar well, tube dilution or microdilution assays.