Hi, unfortunately Fusion don't have a tool like bend/follow curve, but you should be able to get your design done.
There are two main workflows to consider, 3D curve and projections (not only project curve to surface, but in general using 2D data on curved surfaces).
There are some reasons why you may not want use 3D curve. It is essential for complex surfacing, but we could have a lot of trouble to match surface.
That's way I'll focus mainly on how to get desired design with some sort of projection.
First thing we need think through is way did you use term bend? Did you mean that specifically, or you've try to be graphical. I will elaborate this, your
frame drawing was either, raw drawing like you would look straight on someone's face or very specific outline that you would cut and then bend on your mold.
That's not the same because of the distortion that will appear after projecting/bending, that will not only appear but will be differend for bend vs projection.
Take a look on this example (I've used decals and canvases because I can wrap decal on surface)

Main question is did you took that distortion in to acount, when you was drawing your frame?
Scenario A, the anwser is yes (maybe you've made cartonboard model or smoething), and now you need only to wrap that around "mold", in that case best workflow is to use
decal with your design. You need to place it on a surface. To make it propely do in this order:
1. Create "mold" surface alined with document origin
2. Attached your drawing to canvas.
3. Calibrate your canvas to real size and aline with origin.
It should look like that:

4. Apply same drawing on your surface by inserting it as a decal. Now having streight canvas and bended decal match decal to canvas.
Like here:

After we done wraping our design somehow correct, we can use it to redraw design on a flat plane, but our drawing is alredy distorted.
1. Create drawing on a plane that is parallel to your canvas plan, it could be even the same plane. Start your drowing with center line, will use it to keep
design symetric. Draw your curves and apply symetry constraints.

Please use curvture comb to check quality of curve. The idea is to match desired shape with fewer spline points possible. How to judge quality of curve wit comb?
Comb should look like caricature of curve, it may look exaggerated but not differend (that was very colloquially).

Because in this particular exaple I have "mold" surface made out of sigle spline, I will need cut not only frame forehead outline, but also divide
surface to be able to draw and project arms.


2. Create plane that will be perpendicular to previous one. Best would be if that plane could be place in front of surface, like that:

3. To make frame arm we need to do is to project half of frame forehead. To do that you need one more split:

Now we can use it to start and end our new spline. Don't forget to add smooth constraints.

We almost done, now cut surface, unstitch surface, and stitch only frame.


Ok, I had some little problems with last sketch but as you saw I've deleted projected lines.
Now at the end I will say one thing about Scenario B, where your anwser would be no, I did not consider distortion. In that case you doing everything the same,
with one exeption you're draw based on drawing canvas not the bended one.
If that matters in attachments you have my design you can see on shots above.