Take a large plastic bin with high sides, and line the bottom with small deli containers (32 oz suggested), each filled with about 2" of water.
The bin will keep the milkweed stems upright and prevents the water from spilling into your car.
If you don't have enough milkweed locally, go to the edge of town along a country road. The shoulders are mowed mid-summer, causing milkweed stems to grow back as more tender shoots. You can spot them as usually the tallest plants on the mowed shoulders. Find a good clump--you can fill your bin in just a few minutes. Avoid milkweed growing near crops because studies show it can have lethal levels of pesticide. Milkweed grown in partial shade is the best quality early in September.
After gathering, use the bin to disinfect your milkweed and kill spiders all at once. Mix 90% water to 10% bleach (sodium hypochlorite ~ 7%), and soak for 5 minutes, with occasional agitation. Rinse with tap water. You can refrigerate extra milkweed to keep it fresh.If caterpillars are larger than 1/2-3/4 inch, they can find their own way in half a day to a fresh milkweed stalk you lean against an old one. The exception is when the milkweed is dried with leaves curled up. In that case, you need to cut each leaf from the old stalk, unfurl the dried leaf, and hand-remove any caterpillars.
Put the old stems in a small bin and don't discard them for several days. Any caterpillars you left by accident on the old stems will climb up to the top where you can see them.
Be careful not to rub your eyes after handling milkweed.