I guess, depending on the method the OP is using to make her braid, you could eliminate trimming the outside FB edge straight until AFTER quilting.
Leave it be, layer the quilt sandwich (basting with spray, pins, thread, whatever) and quilt.
Then trim the edge straight.

You could also attach the inside edge to the quilt center first - pinning heavily to position correctly - and then trim the seam allowances.

Thanks for all of your ideas everyone! I was also going to add another straight grain narrow border after I put on the bias border so the bias edge would not be the outermost edge. I think that would help also!

I just did a 4 patch posey & did a braid for the border-I didn't do any of those things & sure wish I had/I'm hoping Charisma will work her majic & make it better! Will certainly starch & staystitch next one(if there ever is another) I am so dumb I didn't even realize it was on bias! I am definately a quilt challenged quilter!!

What is stay stitch? Should I know that already? Do I know what that is already and not know that I know that? Did I just say a riddle?

It's just stitching to stabilize the borders - just the quilt top, in this case no batting or backing.
But those stitches will keep the edges from stretching.

Another option is to use something like this - it eliminates the need for the stay stitch (and even the starch, it you really don't want to use it):
http://www.ctpub.com/productdetails.cfm?PC=2359

Here's a suggestion. Instead of making at pattern of a braid, could you make an actual 3D braid and add it to the quilt after it is quilted? It would become the binding and final border all in one. Instead of being made of pieces cut into a pattern, it would be fabric braided, stitched to hold it's shape and then stitched to the edge of the quilt much in the way the Sharon Shambler (have I misspelled her last name) adds some of her borders on her award winning quilts.

This is what I did for the quilt below. In fact because I had just a few inches of extra fabric, I didn't trim it until after it was quilted and I was ready to put the binding on - even though I wasn't working with bias edges (they are strips), the theory is the same.

I use this trick which I've never shared before, sort of a "secret recipe"/personal trick of the trade.

I buy this at JoAnns in the hem tape/rickrack display section and keep several packages on hand at all times.

Jan in VA

That's a really snazzy looking border!

You can also add a narrow 2 or 3 inch border after the braided border to help stablize it. if you do it in the same color as the binding it will blend the two an be nearly invisible. A braided border sounds luscious.

EDIT: @ Jan in Va, You are genious!
peace