Glen, your lauding the audacious tenacity of Bermuda grass reminds me that in one country the dandelion is a weed, and in another it is the dandy-lion and a veritably beneficial herb.
I have taken to simply pulling up as much of the Bermuda grass' lateral roots as possible by hand (to locate the buried rhizome) and using a hooked garden cultivar tool to pull up the crowns. After a rain when the soil is moist and loose it is fairly quick, easy and rewarding work. So, I think Michele's idea that hand pulling can work is true over time.
Of course it can slowly grow back from well-established and camouflaged patches at the edge of the lawn, but it seems like the shoots and rhizomes get less vigorous each time after they are disturbed, and I see a huge difference between planting beds where I have done regular removal and those where there is just mulch to retard them (as in our cacti bed). By now the mulch is nearly buried underneath a mass of B-grass so I am planning to use some tough gloves to get in there and work the cacti bed next year. I'd rather be able to get to the weeds than have mulch keep me from getting a good grip on them. And, I like the way the soil gets aerated at the same time.
Uprooting the Bermuda grass that has infiltrated the lawn and migrated to the edges near the moist flower beds also makes it easier to get DH's support for expanding those beds as new bare-dirt patches open up after weeding! It makes my daylily heart happy to have an ever-widening edge to accommodate more fans in... :D