If you have a sensor that can detect things the size of bioweapon pathogens at concentrations where airborne pathogens would be dangerous, then yes, you absolutely can test for them. And, what do you know, some common bioweapon bacteria are around .5 um, and HEPA filters have to be able to filter out 99+% of objects .3 um to be rated as HEPA bu the US DOE. Add on that many bioweapons are actually not natively airborne and are distributed as aerosols with even larger droplet sizes, 1.5 um to 5 um, and a certified HEPA filter is absolutely capable of defending you from biological weapons. The technology to measure things that small and defend against them is readily available.
God, I hope they don't apply the same rationale to TSA.
"Well, there's clearly no real way to get anything dangerous through here without the metal detectors picking it up, so no need to test our systems with any realistic threats."
The TSA would be completely, perfectly effective if it simply didn't let anybody get on planes. That defeats the purpose of the TSA, of course; they have to let people on planes. Our filter, by comparison, is allowed to stop everything, which makes its job much easier.
* Aerosols are really the only effective way to deliver biological weapons. This holds even with person-to-person transmission; "airborne" transmission almost always means "infected person coughs, spreading aerosolized fluids that contain infectious bodies".
* Aerosol droplets smaller than .5 um don't land on parts of the lungs that can absorb them and are re-exhaled relatively harmlessly. Aerosol droplets smaller than .5 um also lose stability (evaporate, chemical changes, solar irradiation) too quickly to be useful.
"Realistic Threats" are, in this case, particles between .5 um and 5 um. There is zero difference between a droplet with and without an infectious payload. If you really wanted to you could do this test with some completely harmless organism like a household micrococcus strain, but it wouldn't demonstrate anything new. If there are no particles of that size coming through the filter, you are safe, in the same way that the plane would be safe if it took off with no people in it.
Sorry, started thinking like I was writing a paper. Not a Tesla Motors employee. Used "our filter" to separate it from "the TSA's filter".
For the actual question: you probably leave the filter in place until it's clogged, at which point you replace it as normal except you're wearing a hazard suit. Those filters basically don't let anything go. However, note that the filter will be exactly as contaminated as anything else on the outside of the car is; a persistent weapon will have covered every surface in the attacked area with hazardous numbers of spores or similar, not just the filters. If it's not a persistent weapon - that is, it's designed to kill or incap everybody and then dissipate so your soldiers can walk in two days later and take over - then you just wait those two days.