Every Battle Bunny Riven I've seen has flamed no matter what the circumstances are. I have honestly never seen one that was a decent person or even one that was simply quiet in chat.
Some examples of what I've seen...
If they beat their opponent in lane: 'Git gud, noob.' or worse (usually much worse).
If they lose lane: 'Wtf, this guy's hacking.' all game long or 'Omfg jungler, ^^^^ing gank, you useless ^^^^.' etc.
If someone on their team feeds: 'Omfg you ^^^^ing useless ^^^^.' /All 'Report this ^^^^ing noob <champion>.' etc.
I know this may not be the case for every Riven with that skin, but if you exist, you precious, precious creatures, please never be like the ones I've seen. Please, stay innocent and kind for as long as you live. Thank you. :D