For 1/8", I would fuse wonder under to the back of the bias tape fabric and cut out 1/8" strips. Fuse them in place and then zig zag them down. Try this on some scrap, to make sure you can make a tight turn if needed. I don't know how the fusible will act on stretching the fabric in a tight arc. You may have to tug on it a bit first, before you fuse it down.
To temporarily hold the others down, I would use Elmer's glue and then set it with an iron. It will easily wash out later, and if you want to move it? just tug on it, reposition it and then glue it back down :D:D:D