Good info, wombat.
I wasn't familiar with this particular pest, so I looked it up and found out why - so far in this country this bug is only in So Cal and southern AZ. It looks like it is another one of the benefits of globalization, a recent import from warm places like Africa and southern Europe. It does particularly prey on brassicas.
"Bagrada bugs may not be readily observed until damage has begun, so look carefully for fresh feeding damage (light green starburst lesions), which may be easier to spot than the insects themselves at early stages of infestation. Home gardeners and landscapers should carefully inspect their plants and shipping containers prior to planting. A good time to inspect is right after watering when pests hiding in the space between the potting mix and the sides of the container may be flushed out and more easily detected.
When the bugs are common on plants, they may be monitored by beating or shaking plants over a tray or a sheet of paper. More frequent scouting may be necessary when temperatures rise above 75Â°F. Bagrada bugs tend to be most active and visible during the warmer parts of the day; therefore, monitoring should occur at those times. When temperatures are low or on cloudy days, these bugs may hide on the undersides of leaves, around stem bases, or in soil cracks and crevices.
In gardens where the Bagrada bug is present in very high densities, it may be advisable to remove very attractive host plants such as sweet alyssum (Lobularia maritima) and replace them with plants not in the mustard family. Sweet alyssum can attract bugs into the garden and also serve as a source of infestation for other plants in the garden or landscape.
Picking the bugs off plants by hand is only feasible if pest populations are very low. When infestations are heavy, it may be possible to vacuum the bugs with a portable vacuum cleaner. It is often easier to tap the plant onto a sheet and collect/vacuum the bugs rather than removing them individually.
Although spiders and other general predators may feed on the Bagrada bug, it does not have specific natural enemies in the United States. [This is generally why all these imports are so invasive.] Unlike the harlequin bug, which it strongly resembles, the Bagrada bug often lays eggs in the soil, which would render egg parasitoids, such as wasps, ineffective.
There is little information on the effectiveness of pesticides that can be used against the Bagrada bug in home gardens. Generally, stink bugs [to which these are closely related] are difficult to manage with insecticides; and repeat applications are often necessary. The adult bugs usually escape injury by flying away before they contact the insecticide only to return later. "
The only positive suggestion they make is growing things under row cover, tightly fastened down and put in place before the bugs show up, so that you aren't trapping them under the cover with your plants. Even this sounds a little iffy, since the eggs can be in the soil.
Sounds like a really nasty pest. I'm thinking that the hand vacuum is going to become a necessary gardening tool!