Just curious is your lawn wide open sun and what is the most plentiful grass in your area?? If all your neighbors are Fescue lawns you having Bermuda seems a bit strange..
I would go with round up if Bermuda is dormant right now. Be very careful along edges, but round up will only kill what it contacts. I would also apply a crab grass pre emergent such as Prodiamine before soil temps hit 55 degrees. Once lawn starts greening up good hit it with a good blend of slow release fert with higher nitrogen to promote Bermuda growth and spreading..Repeat this every 4-6 week's..
Mowing frequently 3-5 days will also promote spreading of the turf grasses as well as good watering practices.
Now with all that said my best advice is Hire a Professional Company
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