Bermuda grass is not hardy here in the northeast. I also found while researching, that it has a deep and tough root system. I am not sure of the identity of the grass you are calling Bermuda grass, but I do suggest you take it to your local extension office to have it positively identified.
It could be zoysia grass.
Whatever it is, you consider it a weed and do not want it in your lawn, therefore remove it physically by digging it out or use an herbicide on it. Replant the area with desirable grass seed.
Weeds can be carried in on lawn equipment if you employ a lawn service. Weeds can also be transferred into your lawn via animals, birds and wind.