Should I invite my boss to a shared-interest event or just mention it?

So I am working in corporate and as most people know being liked and fitting in with others is part of the culture of working here. Many people have told me to try and be friends with my boss and higher ups as this will open doors working here. I haven't been the best at this and maybe it's because I hate being fake. Not that I dislike people that I work with but I am not a friendship level with them. My boss is cool and I think we are around the same age. I haven't spoken much with her as she is busy but I do have a common shared interest with her. I found out when we were out for a netwok event. So we do occassionally talk about this shared interest and this week I found out there will be some type of fashion event related to this and I know we both took off the same days. So I am thinking is it a good idea to invite your boss to go with you and make friends with her or just let her know about the event?

Should I invite my boss to a shared-interest event or just mention it?
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