She really didn't. Zara was the one who made the snide comments and the one who was gleeful running to tell Liv when Tom had kissed Ellie.
I also find it minimises genuine bullying with how easily that word gets thrown around. No one has bullied anyone in there. There's been some friction, some pettiness, some snide behaviour but no bullying.
If anything Olivia is two-faced and not a good friend, but she isn't a bully.