Answer: Probably the safest route is to get between the fences and dig the unwanted vegetation out, roots and all. I'm afraid any herbicide you use to kill the bushes will also affect your lawn. If you're careful (because of the wooden fence), you may be able to rent a flamer and burn the vegetation out. Wish I had an easier solution! Once you've gotten the vegetation out, lay some weed barrier down and cover it with gravel or bark to keep things from growing there again.
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