Street photography can be a lot of fun...and intimidating! Taking pictures of strangers is one thing that I'm still working through when I walk around different cities. I'm not perfect at it and I often miss opportunities because I'm afraid to ask or pull out my big camera! So in all honesty, I have a lot of growth in this area, but I keep trying it out with varying success.
Most people I've found, don't mind having their picture taken. Sometimes I ask, sometimes I don't--it just depends on the situation. If it's in a multicultural situation, hand gesturing works wonders! I point at my camera and then at them and generally with a head nod from them, I'm cued to take picture!
How do you get over the fear of engaging others, especially if you're more timid? Well, this is me completely and my best answer is pretty simple. Just do it. Don't wait until the perfect moment (because it will pass you by). Just get over your fears and ask! They worse they could say is no...so what danger is that?
If you go for it, let me know! I'd love to hear how it went!