The difficulty of getting rid if bermuda must depend on where you live. I'm finding thick roots 12" deep as I dig. My friend did a BTE garden down the road from me and the bermuda loved it

Within a couple months she was having a hard time keeping the bermuda for taking over her veggies and it seems to be getting worse as time goes on. I have a BTE garden, but there is no grass near it.
LG had a legitimate question...where the chips are only 2-4 in. the bermuda will find a way, like it did in my garden. Where the chips are deeper, it can't really get a foothold..and didn't in the deeper chipped areas in my garden. Then one also has to stay on top of it, which isn't hard to do in the BTE, as one can clearly see the green of the grass against the brown of the chips and yank it out before it gets good purchase.
I think some folks think the BTE garden method is the cure all and there will be no more weeding chores to be done once it's established, but one still has to be vigilant and aggressive towards weeds and grasses there all the same, it's just less frequent and easier to remove them than in a regular tilled garden method.
I let the bermuda take over one corner of my garden only, just to see how easily it was to remove, how quickly it took over, etc. I had seen vids on YT about people complaining that the BTE method nurtures the bermuda and how their gardens were filled with it, so I wanted to do my own experiment on it. I did. I found it was easily preventable by using the correct thickness of chips~as evidenced by the other areas in my garden that DID have the correct depth of chips and was devoid of the bermuda. And I found it was easily pulled up if it did get established, so really no excuse to have it going on in there...just pull it up, replace deeper chips on that area.
It also helps to have some sort of edging on the garden that separates it from the surrounding lawn, though it will still creep in, it won't be as easy for it to do so. I have edging of landscape timbers around my garden and it still managed to make an appearance there but, again, it was so easily removed and prevented that it was hard to see why folks can't seem to deal with it.
On the original vid of the BTE garden method, Paul G. just uses a rake to remove the starts of weeds and grasses, showing just how easy it was to remove them from the chips. Paul walks that garden daily and probably several times daily, so he's able to keep on top of it better than most, but even for those who only get to visit the garden once a week for any length of time, part of that time should be spent searching for and eliminating any upstarts of grasses and weeds. That's just a part of regular maintenance of a garden, no matter the method used.