Obviously this is a challenge. Treating the garlic mustard before bees are active is one strategy, this time frame has passed for this year but should be considered as soon as the plants emerge next year. The thing to do this year is to keep the plants from going to seed by removing the flowers. There are strategies to do this that might not be too daunting to consider.
If these methods are not an option then a compromise
will be necessary. Garlic mustard is a very serious pest. Bees need protection. Those are givens. Treating the garlic mustard plants that
are not flowering with Roundup will prevent the bees
from taking tainted nectar back to the hive. This will only need to be done once. If the garlic mustard roots are killed the seeds that sprout next year will probably be in small enough numbers that hand pulling will be sufficient to eradicate the pest. It will take several years of attention and effort
because of the seeds in the soil but it is possible to succeed.
Here is a link to more information and strategies for controlling garlic mustard in
woodlands. http://www.myminnesotawoods.umn.edu/2010/07/garlic-mustard-a-minnesota-woodland-owners-story/ there are many resources in addition to the feature piece.
Another expert provided this answer 2 years ago.
Controlling garlic mustard is an ongoing process. The seeds can lie dormant in the soil for as long as ten years. Repeated pulling, herbicide or prescribed burn will be required.
The goal is to not allow the plants to flower and produce new seeds. A caution is that even if the plants have been pulled or cut, they can still produce seeds. They must be bagged and removed from the site.
Glyphosate has been used to control this invasive, however it is non selective and will kill everything else that it hits. The recommendation is to leave other plants in place so that the garlic mustard has less opportunity to sprout.
I am including a link from MSU with more detailed information under Management Summary.
This is from Update on garlic mustard biological control an article by Jeffrey Evans and Doug Landis posted on May 18, 2007.
"The goal of management is to prevent garlic mustard from producing new seeds. Most first year seedlings and rosettes will die naturally, so management efforts should be focused on second year plants. Second year plants are easy to distinguish from first year rosettes in late spring once their stems elongate in May and they begin producing white flowers. First year rosettes will not have long stems or flowers and lay close to the ground. In summary, small infestations can be managed with vigilant pulling of second year plants every year prior to seed production or with careful application of glyphosate (e.g. Roundup) during the late fall or winter when most native species are dormant.
We now know that viable seeds can develop on any garlic mustard plants that have already flowered, even after the plants have been pulled. For this reason, we no longer recommend burying pulled plants. Plants should be bagged in plastic, tied up, and removed."
When purchasing and using herbicides be sure to read and follow all label instructions.