Advice on the rude bartender at my restaurant?

Hi, I have been with my restaurant company for about 3 years now. About 6 months ago, I transferred to another location within my company in order to become a server. Before I was a host and food runner. Being a server so far as being a good experience, however something that I am struggling with is this bartender that works at the new location. She is older than me (50s) and has been a bartender there for about 5 years. When I first started working at the new location, the first thing to come out of her mouth to me is that she demands respect from me. Continuing to work with her, I noticed that she is very particular about things. She expects you and other servers to greet her by her first name and say hello to her. If you don't do this, she will call you out on it. She is very commanding and sometimes authoritative as well like she owns the place. I understand she has been there for a while and she's good at her job, but it really put a bad taste in my mouth the minute she started interacting with me. If you do something wrong in her eyes, she will call you out on it, in the moment, even in front of customers which is often kinda embarrassing. She will lecture you about things you are doing wrong and front of others as well. I have been trying to get on her good side by running drinks, getting more ice for the bar, and overall helping her. But, overall working with her gives me anxiety and often makes me feel stupid at my job. I have seen that she talks with other new servers like this as well.

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Any advice and has anyone dealt with this as well?