Preempt Your Fears
"If you have something negative about yourself that you wish to share with others, take the initiative to say it right from the beginning." (Talmud - Baba Kama 92b)
This is an effective tool to use when it comes to overcoming needless fears of other people. If you want to ask a question and are afraid that someone will become angry at you, at times it's worthwhile to start off, "I would like to ask you a question, but I am afraid to ask."
Most people will reply, "You don't need to be afraid. Feel free to ask."