I used to live in Texas and had Bermuda grass...
unfortunately, Bermuda grass roots can go as deep as six feet... but the majority of the roots will stay in the top six inches of the soil. So most barriers won't completely stop Bermuda grass. I recall my neighbor making a 3 foot high raised vegetable bed... and Bermuda grass got into it too. She was so upset!

Forgot to add... I found the best weapon against Bermuda grass to be dense shade. Thickly planted garden beds did more to get rid of Bermuda grass than any mechanical or chemical barrier ever did. I managed to rid my entire backyard of it and had nothing but patio, pool, pathways, and garden beds. It took a good four years of diligent weeding to finally realize I wasn't having to weed Bermuda grass anymore.

You can use a plastic barrier about 12 - 18 inches deep like they use with bamboo (another grass that is a little aggressive :-) ). It will actually work better than concrete and is cheaper. Make sure to slope the barrier to the bermuda grass grows up when it hits the barrier and not down. When the bermuda starts trying to grow over the barrier just cut it off.

Pretty sure bermuda will walk right over the top of that.