Thanks Zoo for the neat GIFs explaining your all-quads fix with the Insert Points + Weld trick. This is a simple solution to a common problem. Many of my designs incorporate precise beveled indentations and seams. When I subsequently subdivide, all-quads topography ensures proper smoothing. The GIF is handy; I save these in categorized folders for future reference.
Going back to Chris Heath’s original question, I’m reminded of a couple of simple techniques that are worth mentioning. Zoo’s approach is the best, but there may be similar situations that can be adequately modeled with a variation of Chris’ original idea: “... I used a bump map. The amount of displacement was however less than what I wanted ....” I use bump maps a lot to get a little extra realism in procedural materials, and sometimes I add a Multiply node to increase the effect. I only use a few Math nodes, and Multiply is intuitive. Dial it up until it looks right.
I'm not sure about starting with the flat disk to model the arrow and bulging it afterward. Maybe less distortion if vice-versa. I have no argument against either the Bulge or Spherify Modifiers, but a lot of times you can get just the right amount of curvature using Soft Selection. In Point Mode, use the Select Tool to select the center point, then dial up the Falloff radius and pull with the Move Tool. Trial-and-error until it’s how you want it. If the Falloff radius goes beyond the outer edges of the surface, it may need to be Split and/or moved back to its original position, then Merged. Not sure what’s optimal in this case, with all the arrow details, maybe curve first and then model the arrow. But Soft Selection is simple and easy to fine-tune. I like that it’s intuitive and precise.