For long term control, shade the area with ground cover, perennials, taller grasses, shrubs, trees, etc. Bermuda Grass needs sun and gradually dies out in shady areas.
Pull Bermuda Grass by hand weekly and remove roots. Maintain an adequate, coarse mulch layer of at least 2 1/2 inches. Plant future competitive plants thickly to eventually shade the ground.
Add barriers, such as steel edging around the perimeter of beds. It will minimize encroachment if the edge is maintained weekly.
On a hot, sunny day, spray 20% food grade vinegar on stubborn weeds that spring up in sidewalk cracks . Be sure to protect desirable plants or the vinegar will kill them, too.