Answer: Dicentra, the Bleeding Heart, is an early spring flowering plant that dies back to the ground in the summer, after it has finished blooming. When the foliage has completely withered and turned brown, cut it down at soil level. The roots of the plant will remain alive, and next spring will produce new stems and flowers.
The bugs you mention may be aphids. If you remove all the dead foliage and stems and dispose of them, you'll probably be getting rid of insect eggs, as well. Other than allowing the plant tops to die down and then disposing of them, you shouldn't have to treat your bleeding heart at all. Next spring it will reappear, with healthy new foliage and lovely flowers.
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