To my students (and others) I call it "playing through the break".  "The Break" being that speed/tempo when you stop using only wrist (be it for rolls or other rudiments/phrases), and allowing bounce.  

I guess the next step--from bounce to ONLY bounce is up for discussion.

I say, anything you can play with wrist, play it that way.

If you to have to play ONE note, you likely wouldn't just throw your stick at it and let it rebound willy-nilly.  You'd play that note with full control of the stick.  Why shouldn't you use the same control when playing many notes IF POSSIBLE.

There may be bits of variation depending on the actual music being performed, but....I think you see what I'm getting at.

The same (perhaps even more so) goes with feet control!

It sounds like you are working on the "multiple bounce" (slang is buzz roll, not to be confused with press roll) which is an entirely different technique than the double stroke roll.  Or are you working on both?  Or are you just closing your dbl stroke with a multiple bounce or are you closing with a press?  Or are you keeping your dbl clean on the close? You need to figure it out because all these options are available to you.  But yes, it's good practice to start slow, work through your transition points, close your roll and then slow back down.

A few of the guys here including myself have had TONS of snare lessons and I'm really not a teacher so take my advice with a grain of salt- but I can pull pretty clean dbls on my kick and do allright with 5 stroke/6 strokes/sextuple dbls/ stuff like that.

I sorta try to "moeller" with my feet and you need good control with your heel as well (to keep beater from splatting into the head)... all I can say is practice.  This technique is tuff to pull off in loud volume situations, but if your kick is triggered you could probably get away with it.

The faster I get on a kick drum the more I realize how much time I've wasted.  It just seems like I could have spent my time going in more effective directions with my playing.  JMHO

multiple bounce rolls are used more in concert snare applications.  I don't really use them, cause in an amplified setting they don't cut very well-  you can get them to work in acoustic/solo situations.  A "hard pulled dbl" or press roll is usually my weapon of choice when I want the effect.  But in rock a dbl is just so fast and the louder your band/bigger the room- you might want to not really go much faster then 16 th notes if you wanna cut thru.  YMMV  Less is for more.  More is for less  

I like the comments here.

Jon E, that's good that 'Spaz Mode'. Might be a good name for a punk band. Yeah, and I think we all know what you mean.

I agree with felix on the hands. I like the power of an opened double stroke with the accent on the second, use the fingers the whole way, and modulate speed to give effect.

 A nice thing is to start with a steaming press roll and control it into a double that slows just a bit to chop it off. It gives the ullusion it was a double stroke all along.