|Across the front of my house, I have a bed that has burning bushes and 2-3|
|There are a couple of methods you can employ to remove the weeds. One is a contact vegetation killer (such as Round-Up) and the other is a device called a flamer. Spot treating with Round-Up will concentrate the herbicide on the unwanted weeds and kill them completely. A flamer is a device used to burn the weeds out, which generally kills the roots, as well. Once the weeds are gone, use a weed barrier, plastic, or even several sheets of newspapers laid out over the area. Cover with rocks and you'll never know it's there. To make very sure new weeds won't pop up, you could first cover the cleaned up area with a pre-emergent herbicide (to stop weed seeds from germinating) and then cover with weed barrier or plastic.
Best wishes with your garden bed.