I have had *some* success with this, though it took me a couple of years. There are a few things that I have learned that might be helpful.
Bermuda grass is impossible to pull from compacted or hard/dry soil. It just breaks off at the ground level. It is much easier to pull from wood chip mulch, and even easier from compost. From the mulches, you can "easily" remove incredibly long ropes of root/rhizome.
In my soil at least (described below), the bermuda grass roots prefer to grow into the mulch than into the soil. After a year mulched with wood chips, most of the roots migrated into the chips. There may still be some down in the soil, but they seem to be small and weak.
I recommend against planting perennials your first year, since pulling the bermuda grass roots may disturb them. If you have to dig the grass out of your beds the second season, you don't want your perennials to be in the way.
Once I established a bermuda grass-free zone, I seem to be able to control the edges with a shallow ditch, with mulch on both sides. I consider the deep mulched area on the grass side of the ditch to be my future growing area. Whenever I see rhizomes or roots try to cross the ditch, I can pull them back pretty relatively easily because of the deep mulch on the grass-side.
Basically, my process going forward will be to deep mulch an adjacent area and let the grass grow into it, using the ditch to keep it out of my garden. Then, after a year, I can expand the garden area by either removing the remaining mulch (riddled with grass roots), or pulling all of the roots out of it, and moving the ditch out 4 feet. Then mulch another 4 feet beyond that.
I have fairly compacted soil, and a shallow water table. Humid subtropical, with a fair amount of rain. I've not done any soil testing, so I don't know how the composition, but I suspect it is mostly clay. It does not drain well. I mention this because it might affect how deep the bermuda grass roots go.
