Bermudagrass is very difficult to control especially within a lawn setting. Many sources report that cultural management without herbicides is not possible, but here's what I did find for management information to try in your non-lawn areas:

"Bermudagrass grows best when irrigated. If the area where the bermudagrass is growing can be dried in summer without injuring any nearby ornamentals, withhold water to dry the stems and rototill or spade the area two or three times during summer months. This will bring rhizomes to the surface where they dry out. Raking to remove rhizomes and stolons will also help... Be careful not to cultivate bermudagrass if the soil is moist or the weed will spread, because cultivation chops the stems into segments and each segment becomes a new plant. While cultivating and drying can effectively kill established plants and rhizomes, they do not kill seeds in the soil."

"Bermudagrass growth can be reduced by increasing shade from trees and tall shrubs. Shaded growth will be fine and spindly; plants are easier to remove than those growing in full sun."

Be sure to put any plant material that you remove in your municipal waste and not in your compost as most home composting does not get hot enough to kill the stolons, rhizomes and seeds.

"Mulch can be used in a variety of ways to manage bermudagrass. Black polyethylene applied over bermudagrass to prevent sunlight from reaching the plant can effectively control established plants. Mow and irrigate the grass, place the plastic over the plants, and leave it for at least 6 to 8 weeks in summer. Placing plastic over bermudagrass in winter will not control it. Be sure that the plastic remains intact without holes, or bermudagrass will grow through the holes and survive. If ornamentals are planted in holes in the plastic, bermudagrass control is reduced."

https://ipm.ucanr.edu/PMG/PESTNOTES/pn7453.html

The publication that I link to here also includes information about solarization. This process tends to be more effective in other regions of the country, but not in Michigan for perennial weeds like Bermudagrass.

Best of luck with this challenging weed! If you want to see some real life examples of Extension Master Gardeners managing this weed, you could stop by the Grand Ideas Garden and talk to the gardeners there. I know they are regularly combatting it there. https://www.facebook.com/GrandIdeasGarden/