Hello Margaret,
Star of Bethlehem, Ornithogalum umbellatum, is a non-native, noxious weed that is very difficult to control. If it were growing in the lawn, you would have more control measures, but since it's in a garden, you have limited options. Using an herbicide would only provide limited results. 

In the landscape, the best control method would be to dig up the plants when they are just emerging and dispose of them in the trash, not in the compost bin. You should also dig 6-8 inches deep and that area and remove the small bulbs that remain in the soil. You might be surprised at how many bulbs a single plant can produce. This is not a one-and-done task. You have to be patient. 

The following are three sources that I have found that provide management information for Star of Bethlehem.
https://hyg.ipm.illinois.edu/article.php?id=1271 
https://extension.wvu.edu/lawn-gardening-pests/weeds/star-of-bethlehem
https://www.canr.msu.edu/news/homeowners_battling_a_weedy_orchid_invading_lawns_and_flowerbeds

Please keep in mind a few things if you choose to use a herbicide: Make sure to follow the label instructions and cautions; Check the label to see if Star of Bethlehem is listed as one of the weeds the product kills; The product may kill the existing plant but probably not the many bulbs left in the soil; The product can probably kill nearby desirable plants if the spray hits them; and finally if a specific product is mentioned, it is for general information purposes only and not an endorsement by MSU Extension. 

I hope this information is helpful. Please let us know if you have any questions or need further information.

Have a great Spring!

Thank you so much. We’ll dig away. 

Good luck and I know you'll have a successful outcome.