Bermuda grass and zoysia grass both are invasive varieties that will take over neighboring yards and planting beds if given the chance. Bermuda is a fast growing grass, while zoysia is slower to spread. There is no single product that will kill one without also killing the other, but there are things you can do to discourage and slowly kill off Bermuda grass while leaving the neighboring zoysia intact.
Decrease lawn feedings to no more than two a year. Bermuda grass requires more fertilizer than zoysia.
Reduce the amount of nitrogen in your fertilizer. Bermuda prefers higher amounts of nitrogen than any other grass.
Cut the lawn to a higher height—about 3 to f4 inches high. Bermuda grass prefers shorter blade height and the higher zoysia grass will steal much needed light from the Bermuda grass. This method is slow, but highly effective.
Plant shade trees and shrubs in your yard. Zoysia is shade-resistant, but Bermuda grass needs an abundant supply of sunlight and will die off in shady areas.
Apply a glyphosate-based, all-inclusive vegetation killer to the entire yard to kill off all grass and replant with zoysia. You may lay zoysia sod for a quick yard or plant well-placed zoysia plugs over the whole yard.