//"She knows the 'speak' cue already."//
i have sort of learned the hard way, that we humans should teach the "SHHH!" cue FIRST,
AND THEN
begin rewarding barks, rofl.

I did teach my dog "shhh".
It's a cue that needs much much reinforcement, well, it did for my dog. Barking is an irrisistable urge in dogs, and
depending on why they are barking will impact your success as well as the methods you will want to use.
anyway,
i did this--
FOR YARD BARKING, or house barking.
There's probably better ways to teach this,
but, this worked for my dog.
This is indeed, a lesson you will have to re-do now and then,
til dog solidly understands what "shhh" means. Teaching this takes time.
AND MULTIPLE MULTIPLE lessons.
It is hard for dogs to not bark,
so this is something you to teach and reteach, many many many many times.
I got bag of tiny treats, and clicker,
and
sat down outside
right next to my dog,
who likes barking through his fence at passerby dogs.
When he'd bark, i'd give cue, "shhh!" which sort of startled my dog into brief lapse in his barking.
I heavily praised and rewarded
that brief lapse.
Yes, yes, i had to repeat it many times,
of course Buddy resumed barking!

absolutly!!!!! soon as he was done swallowing his treats, BARK! BARK! BARK!
so i repeated my "shhhh!" and rewarded that brief lil moment of no bark....
i offered him praise and lil back rubs and praised him,
nonstop,
the whole time he was silent.........(my dog LOVES praise)
over
and
over.....
but,
eventually,
my lil einstein dog did begin to realize,
"ohhh, when i STOP barking, i get love and Liver Cookies? ohhhh"
It was a while til i could add in a click, as i found it hard to time the click well at first, when his lapses were pretty brief at first.
I had to spend much time on this cue. I did this often, several times a day, every day, for a long time.
Overtime, i was able to wait for a slightly longer pause in the barking til i rewarded.
Sometimes, i had to REtrain this, spend some lessons all over again,
if Buddy began getting sloppy about barking a lot.
Now, i can stick my head out the door, and call "shhhh!" and Buddy stops barking.
Lol, overtime, Buddy and i have settled on a 2 bark limit.
He seems able to count,

ha ha, cuz i say nothing for two barks, but, on 3rd bark, i'll call out "shhhh" and that is the end of that barkathon. Adorabley, i know you won't believe this, but, my dog seems to know this, and now,
he usually only barks twice as dogs pass by his house. for real, two barks. which is okay with me, sometimes they are his pals, he's just saying "Fluffy! HOw are ya! Ey, it's me, Buddy, over here! so excited to see YOU! Hello!" in his two barks to pals going by.
TWO BARK LIMIT at my house, lol!
You might want to consider, not having dog outside in yard***
unless you are free to run out there and assist him to stop his barking and help him learn the new cue. (***if that is the scenario you are working on??)
Barking is self reinforcing,
and if your dog has periods of time
where he can
bark his lil head off, uninterrupted,
that will make it all the more difficult for you to teach the cue.
GOOD LUCK!!