It’s hard to give you a definite answer because you don’t give much information to go by and what you do say might be you misinterpreting her behavior.
Firstly, and logically, if you care about her and when she’s alone with you she seems to care about you, then talk to her about it. You are calling her a showoff. What about “ignoring” and “being bossy” amounts to “showing off”?
Let’s take ignoring first. When she’s with her friends it cannot be the same as when you two are alone together. You can’t have her undivided attention. Maybe this bothers you more than it should or maybe she really is ignoring you. I can’t judge that without being there.
As for being bossy-What does she do that is bossy? Command you to do things for her? Or ask in a way that’s polite? Do you think she’s making fun of you? Trying to make you look subservient? What are you ideas about equality in a relationship? Are you the type of man who thinks that the man is the “boss”? Are you being too sensitive, perhaps? I’m not saying that you are. Don’t get me wrong. I’m just trying to get a little more info to go by as well as asking you to look at your own behavior.
Now, as for “showing off” we all have different ideas about what constitutes showing off. Some people are really comfortable and extroverted when out with a group. They get louder, funnier, more animated. It could be called showing off or it could be accepted as a vibrant personality. (Some people say bubbly, I hate that term!) If that is her personality and she means no offense to you, then maybe she’s not the girl for you.
But do talk to her if you care about saving your relationship. Calmly explain to her what things you find disrespectful and annoying. I don’t think it’s fair to say that a person has to be the same when you’re alone vs. in groups. It’s a different social dynamic. At any rate, she will either be willing to change or not. Then you go from there. A positive relationship needs to have respect flowing in both directions. Make sure you respect her for who she is and that you ask for (I don’t want to say demand, it sounds bossy) respect in return.
Good luck!