Backyard Orchard Weed Control? I like fire.

Q. My backyard is planted with a 20 tree fruit orchard similar to a small scale UNR orchard or Dave Wilson backyard orchard. I have added many truckloads of the free mulch from the orchard over the past 3 years, which has broken down and made the soil much better. The problem is last year I got overrun with bermuda grass. I put cardboard down, more mulch down, and the grass just came up through it. Do you have any tips on getting rid of it naturally? Is there any type of green mulch I could plant in the spring that would choke it out? What do you guys do at the orchard to keep the weeds out?