"I went to a dance party with my boyfriend at a chain studio around my house last night. While I was there, a woman teacher who was extremely new to dancing openly and obviously started hitting on my boyfriend of nearly 3 years."

It very well could be a problem and a reson not to go back.

Keep in mind though that some people are just always a bit flirty, without necessarily intended to follow up on it. It can just be an aspect of a super-outgoing personality (though you did say she was cold to you).

It can also be a part of promoting the studio and trying to sell lessons.

The most important question though: what did your boyfriend think of the whole situation? More than anything that actually happens, how well you handle and communicate about it together is what really matters.