But the Roundup that is made to kill grass, will kill pretty much anything. Bark may offer some protection from direct spray, but when you spray it all over the ground around the base there is a good chance it will get picked up by the roots and significantly damage or kill the tree.

I would go to a nursery or call an arboretum and ask what they would recommend. I haven't tried black visqueen, but I do use landscaper fabric all around my gardens to keep both the weeds out from new seeds and prevent any seeds already in the ground (like thistles) from coming back up. Layer on a good thick layer of mulch and the lack of sunlight usually kills what ever is underneath the fabric. I imagine the black visqueen has the same effect, if not better. My only worry would be water absorption around the tree. Water will absorb through the landscape fabric, but won't penetrate the polyethylene.