True Bible-believers shouldn't need to bring up God all the time. Our testimonies should speak for us, so that people ask us about our faith. We CAN talk to people about God, but we shouldn't be pushy. Some people don't want to hear it, so they need not be bothered again (at least not for a good long while; some people do change their minds on such matters).
The reason I'd want to spread my beliefs is because I believe if you don't have a relationship with God, you'll end up in Hell. It's harsh, but that's what the Bible says.
Now, I'm not going to go up to an atheist and say, "Get saved, heathen, or God will damn your soul in eternal fire!" That would be absurd. (Cough cough *Westborough* cough cough...) But if someone asks what I believe, I'll tell it to them straight.
Thank you for being reasonable, and I hope I too have been.