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I have a male and a female holly bush which have attracted flies thru the summer and now have both flies and wasps. Thousands. While they are not harming the plants, they are in a place where people have to pass and they are making them nervous.

Any suggestions on what I can do to rid the bushes of the flies?

Your problem is almost certainly some kind of insect... aphids, scale insects, mealybugs, and some others exude "honeydew" a sweet sticky secretion which attracts the flies and wasps. Given that it is holly and given the magnitude of the problem, scale insects would be my guess, but that's a guess. You need to inspect closely and find out what insect you have.

Deal with the insect that is secreting the honeydew and the flies and wasps will go away.