
I rendered "начальство" as "the bosses".
Could we also translate that as "the management"?
i.e., "And where is the management?"

The Russian word freely refers to anyone above the speaker(s) in the work hierarchy. Does "management" fit that, then?

Yes, I believe so. It means all those who run the company.
But I'll leave it "bosses" then, to be on the safe side (otherwise, the reader may not understand the sentence correctly).

Not necessarily those at the top; one's direct boss(es) would do, too. So "bosses", being apparently a more general translation, is perhaps more useful.
Heck, it can even refer to just one boss as well - in a little bit familiarising way.

Спасибо, Денис!
> it can even refer to just one boss as well - in a little bit familiarising way.
That's what I would think when hearing "где начальство?".

@Eldad
So, could you please add a variant with "one boss"?
"And where is the boss?" – "At dinner".

Done.

Большое спасибо. :)

Не за что :)