Apply with next style is the correct way to do this.
But the number of paragraphs needs to be consistent.
And with the Professional Skills bullets they need to be named
PS Bullet 1
PS Bullet 2
PS Bullet 3
But there's no way for InDesign to know if a Bullet style is finished and not apply the last bullet style.
So basically - I don't know of a way to do this.
I don't think you'll be able to automate this other than by script, and maybe not then unless there's alread some formatting difference you can key on.
You could format blocks at one time, though, if the bullet style is next style for both the heading and itself, by selecting a heading and the following paragraphs up t the next heading, then right-click the heading style and choose Apply Style and Next Style.
Another thought that occurs to me is that if each block is a separate text frame you can apply the styles using an object style.
If the final document need only have two paragraph styles, Head and List, and each heading ends with a colon followed by end of paragraph, then you could apply List to the entire document, then find/replace for the colon/line break to apply the Head paragraph style.
(If there are other paragraphs within each resume requiring a different paragraph style then this won't work, unless you can find a way of targeting those paragraphs as well.)
Edit: "forced line break" changed to "end of paragraph"