Charmed condition offers no increased charisma bonus, just advantage:
A charmed creature can’t Attack the charmer or target the charmer with harmful Abilities or magical Effects.
The charmer has advantage on any ability check to interact socially with the creature.
I think you are confusing charmed condition effect with the Charmed Person spell, since the spell uses the term Charisma. But it's just advantage, not a Charisma bonus.
From the game:
Magically charm a humanoid that you can see. A Charmed creature can't harm the charmer, and the charmer has advantage on Charisma checks against the creature.
And the RAW for a lot of spells don't really mention what happens if a save is failed on a non-attack spell, BECAUSE for story reasons. A real world example (I know, I know, fantasy world, video game, whatever) it'll be like you walking into a bull pen, that's holding an angry bull, and trying to befriend the angry bull. The bull can ignore you and just stay there, walk away, or charge at you. In the Deep Rothe case, it succeed it's save throw, had the wisdom to know that something around them was doing something to them that it doesn't like, and that someone isn't it's normal handler (if there was a handler), and attacked at the first thing it saw.
there was no saving throw shown on the Deep Rothé when I cast it.
Now that's a bug right there! Not showing a saving throw occurring/happening.
So, what it sounds like happened is you used Animal Friendship, the Deep Rothe passed it's saving throw, but the screen did not show a saving throw was being done, the beast became hostile. With the bug being no saving throw being made was shown.