Answer: First let me say that it will be surprising if the centipede takes over the bermuda in sunny areas. In the shade bermuda suffers more that centipede, but in the sun and with occasional dry times, the bermuda should be the stronger turf species.
Anywhere the turf gets thin, weed species like Dallisgrass can germinate and crop up. Long term solution to most weed problems is to build the densest, healthiest turf through proper mowing, watering and fertilizing. However, a perennial weed like Dallisgrass will compete and survive well once established.
There is not a product that will kill the Dallisgrass without harming the Centipede. Your technique of spot treating with Roundup is effective for eliminating a few perennial weeds here and there, however, you have experienced the drawback of turf damage from spray that reaches turf leaf and runner tissues.
Some gardeners use a wiper or wick type applicator to more carefully spot treat the weed without harming the grass. These applicators are available at many garden centers or home and garden supply stores.
Thanks for your question!
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