I can only tell you what was a breakthough for me. (And also that bumps means practice, practice, practice - I've been seeking out and skiing bumps alot over the past couple of seasons and I'm seeing slow, gradual improvement. But you have to be willing to get in there and keep at it).
That said, my breakthrough was from the Lito Tejada Flores instructional video - Bumps and Powder.
To answer your question - yes, you turn somewhere near the top of the bump - the exact spot doesn't matter. There are lots of possibilities. But if you turn at or near the top, there is less resistance since part of your skis will be off the snow, so it's easier to initiate a turn. It makes sense.
My "Lito breakthrough" was in his concept of a "delayed finish". That is - you don't want to turn quickly and all at once. If you do, it means you will be trying to finish your turn on the steep front side of the bump (a very awkward place to be as a beginning bump skier). You want to start the turn, hesitate for a moment
in the fall line, then finish the turn on the back side of the next bump.
He has a drill on flat groomers where you start your turn, go straight down the hill for a moment, then finish. Start, go straight, finish. That feeling of hesitation is what put me over the top with bump skiing. I know it's a little different from some of the other things said in this thread - but there you have it. Worked for me!
I imagine as one gets more accomplished, you finally get to the point (as some indicated earlier in this thread) where you feel like you can just turn anywhere and ski the bumps almost as if they aren't there. But I know I'm definitely not there yet! So I'm in transition somewhere - an improving bump skier. But I do know that I'm now to the point where I really enjoy skiing all but the gnarliest bumps.
And it was Lito's strategy that worked for me.
If you can't visualize what I'm saying, I can't say enough good things about that bumps and powder video. I'm sure it's still available . . . .