Here is our page on hairy bittercress.  This is a winter annual and produces many seeds. In a vegetable garden or ornamental bed, hand pull and do not let it set seed. It is pretty shallow rooted and easy to pull. Keep the ground covered with newspaper and mulch and try to manage the weed culturally. No herbicides are recommended in a vegetable bed. We are not aware of herbicides labeled for ornamental beds. https://extension.umd.edu/resource/hairy-bittercress

Marian

 There are no easy answers. Post emergent herbicides that list hairy bittercress on the label are for lawns not beds. The label is the law. 

You can look at the label of Preen, active ingredient trifluralin to see if hairy bittercress is listed on the label. However, this is a preemergent and would have to be applied before the weed germinates.  This is not a post emergent and would not control the weed once it germinates.  Also, you would have to make sure the plants in the bed are listed on the label.

Marian