One of the great things for me is the distance I can travel under my own steam!
Bikes are more reliable than you think, punctures can be fixed at the roadside, and if I really need to bail I could probably call my wife to collect me.
Build it up slowly, concentrate on enjoying it, and the confidence will come.
Like the poster above I have been offered help. I had a puncture on a small country road, with the temperature hovering around zero. I was changing the tube and a car stopped to offer help. Despite my reassurance that I was ok, he asked several times and hung about for a few minutes, which was very kind of him.