I will tell you now that a garden tiller is NOT the way to remove Bermuda grass. There is no "raking it out" after you've cut the rhizomes into a billion little pieces with a tiller. If you're like me and water deep and infrequently, plant roots run deep. And every one of those deep little pieces sliced off by the tiller is a potential root for a new stalk of grass. I used a tiller a couple of times when I moved here, but I eventually sold it. I attack the garden with gloves, a wheelbarrow, and a spade fork, and I dig Bermuda out by hand.
What I discovered last winter is that if you go into the garden on a winter day, when the Bermuda is still dormant, that the soil, after a rain or a freeze is like a crumbled piece of cornbread or dried up cake - it is kind of flaky and a bit dry and the Bermuda roots are robust, holding onto the plant energy under ground, so they're much easier to pull out. And they kind of slide out, in big chunks, not just bits of the roots leaving the rest behind to sprout later. If you have the discipline as a gardener to go out when the conditions are right, you can eliminate a lot of the problem come spring when it starts sprouting again. By then, they've stretched out to new roots, tender, breaking off at a simple tug, leaving behind enough to start several new bunches of Bermuda for each handful you pull.
Hands-on is a generally good idea in the garden - handle the plants and pluck off instead of spraying pests you think might be there, and hands-on for removing green pests like Bermuda when they're at their most vulnerable.
Off my soapbox . . .