If someone is singling you out to be on the end of unpleasant behaviour it absolutely can be classed as bullying.
You're almost me in this scenario, although I've been there over 20 years and recently promoted.
We have a lady who wants to poke her business into everyone else's and has an opinion on everything.
She's also rude to those she sees as beneath her.
She's very dangerous and thinks she's "in with management"
Since I've joined the management team I've realised exactly how nasty she is. As in running to the management team snitching on everyone, gossiping and basically being the horrible person we always suspected her to be.
The one manager who listened to her retired recently and she is now passing her info to others including myself.
She's not happy as been told we don't want to know, it's not her business and down the route of her being dragged to HR
She still has her job but currently on best behaviour as we no longer wish to engage in snitching.
My only advice is smile at her and ask her to repeat herself, ensure others are around as she won't want to repeat nastiness. It's said for effect at the time.
Also ask nicely, "are you aware how rude you're coming across"
Another is "I'm not sure I understand your point, can you explain it a little more clearly?"
I would also mention it to your direct line manager, they are usually aware of people who are full of self importance and can't really do anything without a formal complaint.
Bullies never win, they show their true colours