I suggest using a fluorescent dye and monitoring uptake by fluorescence measurement, preferably by confocal fluorescence microscopy. It is 1000 times morse sensitive that spectrophotometry. A fluorescent dye with amine reactivity, such as an isothiocyanate or succinimide ester should be able to label proteins on the OMVs. Many such dyes are commercially available. You can pick one with the desired wavelength spectrum.

Thank you Adam. I will look into those dyes. Will you suggest PBS as a labeling buffer or something else?

PBS is a a reasonable choice because it lacks amino groups that could react with the dye. However, it is usually recommended to use fresh 0.1 M sodium bicarbonate which, being a bit more basic than PBS, increases the rate of the labeling reaction.