Here's a decent example of a double stroke roll. It's played as four 1/32 notes during beat 4 every other measure. Steve Gadd of course
https://youtu.be/ABXtWqmArUU
Nothing wrong with your thinking on this. There's a couple of ways you could play this.
If for instance you start the roll on beat 4, just double up 4e+a to 1/32 notes,
4--e--+--a---|1 2 3 4
RRLLRRLL|R 2 3 4
But at 120bpm I prefer to play it as a 1/16th note triplet starting on the left hand. Just play an 1/8th note triplet and double each stroke. It's easier and smoother to execute but still sounds fast enough. Try it
4...trip.let|1 2 3 4
LL.RR..LL| R 2 3 4
Playing double stroke rolls usually means the drummer needs to make a decision on what type of double stroke roll fits the tempo. Generally speaking, the faster the tempo, the shorter you can make the roll, so a five stroke roll may fit better than say a 9 stroke roll.
And for a slower groove, an 11 or 13 stroke roll might fill the space between the beats better, whereas a 5 or 7 stroke roll could sound too slow with too much space between each roll stroke.
So don't just learn the double stroke roll, learn the rudiments that involve double strokes so you can use the appropriate one. 5, 6, 7, 9, 10, 11, 13, 15, 17 stroke rolls.