For hiding your tweets you have to make your profile setting private. Frist of all log in to twitter.com then go to setting on top right menu, then go to account at the top left menu, next click to protect my update at the bottom of the page. After making these changes you will receive email if anyone wants to follow you, anyone can see your tweet only if you will allow them. Hope these will be helpful for you.

You can't hide your tweets from your followers. If you approved them as a follower - they can see your tweets even if your settings are private. https://support.twitter.com/articles/14016#

If you are conversing with someone - that doesn't mean your comments to them are in everyone's stream though they are on your profile page of tweets. People would only see those comments on their stream if they are following both you & the person you are chatting with. If they went to your profile page - yes they would see the conversation but it isn't flooding their stream they view. https://support.twitter.com/articles...e-they-appear#

I think so you will find the option in the privacy setting in the setting options. Where in you can set the privacy for tweets as well as the followers.