bob
It's better to have two hands than one glove.
I would take a dead on straight photo and measure the distance between the top of the arc and bottom. I'd scale it up and make my copy fit. Since you are doing script, it will be easier as the letters will be upper & lower case and won't show if you are a little tiny fraction off.
And that wouldn't work. Unfortunately you're working with a three-dimensional object that isn't flat, it's curving horizontally as well as vertically. That being the case, a simple straight on photo isn't going to do you a lot of good. You need to flatten the object and layout the lettering on that flattened image. As I said before, paper template is the simplest way to do this.
It's a little trickier since the only outline you have is the top of the bow. Never fear, tape a piece of paper to this area large enough to cover the area to contain the lettering and then some. With a Sharpie or something scribe the bow line on the paper. If there's a strake line below the bow then scribe that. If there isn't then make your own with a flexible rule of sufficient length.
Lay the paper template flat, the floor is good, and put a 3x3 Post It, a 2x3.5 business card, or any other rectangle of known dimensions on the template reasonably parallel to whatever passes for level on that template.
Take a picture of the template as straight on as you can manage and with the Post It or whatever you used square to the image.
Import the picture into your software. Draw a wire frame rectangle exactly around the rectangle marker in the picture, that's why you wanted it parallel to level and square to the image. It saves having to rotate the image to get it square . Map, powerclip, mask, or whatever you use, the picture into the rectangle. Make the rectangle whatever size it is in real life. Unmap the picture. Now you have a full size image of a pair of lines that represents the bow flattened out in two-space.
Layout the lettering according to the lines you scribed. No matter how weird the result might look it will fit precisely. If you did everything right.