Bermuda grass uses an aggressive system of overground runners and underground rhizomes to spread and establish itself. This sturdy and vibrant growth habit makes it an ideal grass in less than ideal soil conditions or when establishing a lawn on a budget. It also makes it difficult to control its spread without regular maintenance. As most herbicides strong enough to control Bermuda grass will wreak havoc on your flower bed soil, manual removal and physical barriers are your best bet.
Rip up the invading Bermuda grass runners heading into the flower bed by hand. Gather the thickened plants pulling them up and towards the direction they are growing from. This will remove the bulk of the runner and rhizome. that is heading into your flower bed. Do this with gloved hands and have no fear of being aggressive.
Weed the flower bed regularly and never go so long between weedings that the propeller shaped seed heads develop on the Bermuda grass as this will exacerbate the problem.
Run an edging tool between the lawn edge and your flower bed once a week or every other week to keep a well defined diving line and small gully between the two planting areas. Whether you use a manual, gas or electric powered edger just use it regularly to prevent an invasion from occurring.
Install permanent garden edging as a physical barrier between the flower bed and lawn. Choose solid stone, concrete, wood, metal or plastic material as for best effect. Remove all Bermuda grass on the edging line and dig a small trench for wider stone edging or simply pound thin gauge edging into the soil with a mallet.