You're right, they're there in their entry under Rogues.
In my defense, the very first line of their entry reads "The bard is an optional character class..." In my paper copy, the entry is in light grey, which meant that I skipped over it, though I see that in the last printing of the 2e PH, the light grey was dropped so it wouldn't appear to be optional.
It's not going to happen as a class of it's own in DC, though you can approximate it with a fighter/magic user/thief (this can be renamed to "bard").