I have turned many a quilt top on my long arm. If it's just the borders they are already secured because I baste down the edges as I quilt the body. My backing has been squared prior to loading the first time.
Remove the top-turn and secure one side to your leaders. If it's a large quilt then I usually will only attach the top to the take up leader and drape the rest of the quilt over the backing/belly bar. With one hand I push the quilt part that is hanging down down, around and under the backing/belly bar and pin. Do this several times to hold it. The weight also helps hold the top.
Now stitch the first border and remove the top when that is finished and repeat for the last border.
You can also pin each unfinished borders edge to the take up and backing/belly bar and roll.
I hope this makes sense. Do not make it too hard because it does work.
My disclaimer is: If the length of the quilt is longer than your longarm rails-it is harder. I also have trimmed back the batting a bit so it's not so much in the way.
Let us know how it all "turned" out.