My bicycle

I have just bought a bicycle. It's pink and it has a basket and a bell and I love it. When I ride it, I feel 10 years old again, and it's a loooong time since I was 10 years old. However, whilst the part of suburban London I call home could hardly be described as the mean streets, every time I go on an actual road on my bicycle I come quite close to soiling myself in terror. Now I remember riding my bike as a kid, and I know I didn't give a shit. I wasn't scared of cars, people, trees, or windows. I should have been though, I took chunks out of my face in various accidents. Still didn't care though. Nowadays, before even leaving the house I put on my helmet, high viz jacket and reflective ankle straps. I'm a vision, as you can imagine. I go out, start off tentatively and gradually build up speed. And then I hear a car somewhere in the distance and my heart races, my mouth dries, and I. Just. Stop. I think some caution is necessary, but I also think I have to force myself to build up confidence. Any tips for this cycling neophite?