Please stop thinking of your reputation.
A healthy regard for the opinions of others is something every social creature should have, but it is almost never a good reason for a lady to do something or to fail to do something.
If you live your life based on what others will conclude from your actions you are not living your life, you are living the life of others expectations. And that is a hollow sort of thing.
It is not to say that a lady should not behave, but it is to say that in determining how to behave a lady regards her own high opinion of herself rather then what others might think.
She also does not desperately try to raise herself in the regard of others. Having conversation and generally being interested in people is one thing, catering to someone's desire to the exclusion of your own is not at all charming and likely to offend.
Remember that you are a lady and above such things. If your company alone is not enough to get you in to social circle you wish to join, then those circle are unlikely to be terribly interesting. One thing every lady understands is that people, be they famous and wealthy or poor and unregarded are not fundamentally different from her. Because she know this she is better off not spending time with people who are busy believing that they are somehow better.