<p>I've got a bracelet concept that I've sketched up as a flat design. I'm trying to found a route by which I can extrude this into a 3d object (depth map?), curve it into a bracelet, then ultimately create a STL file out of it. I'm having trouble finding a way to do this that allows me to "warp" the flat object into a bracelet before I try to print. </p>

<p>Is there a recommend technique for this? I'm not worried about representation of the picture; it's effectively meant to be an 'etched' pattern.</p>

This may not be your cuppa tea, but if you're willing to learn to use
OpenSCAD
or already know how, there's a
Thingiverse
post that appears to directly address your objective.
Correction, this particular post on Thingiverse consists of a series of Python files, of which I have zero experience/qualifications. It may still be of value, if you are Python capable.
Another resource that is strictly OpenSCAD is from Eric Buijs, a rather talented 3D design person. His YouTube channel has a number of useful tutorials for both OpenSCAD and Solvespace.
This video
in particular describes applying a flat object to a curved one using OpenSCAD, resulting in a lithophane.
As I created this answer, I did not re-watch the 12+ minute video, but I recall how he explains clearly how the program dissects the surface into a number of flat panels and then superimposes the image on each segment. From this presentation, I suspect one could expand to a full cylinder.