Don't get caught with a flat

This morning I biked to and from my bike workout and I often found myself staring at the salt and rubble on the ground with some anxiety... what if it blew my tires?

When I'm just riding around town on errands, I am only ever 1-2 miles from home or one of the local bike shops. So if I were mid-ride on my way to get groceries or something, I'd get off and walk it. But I am terrified of getting a flat mid-race. Terrified. I'm terrified of getting a flat period. I've heard tubes blow and it has the tendency to sound like a gun shot... and I jump approximately 10 feet. I've also heard stories of cyclists getting flats going 30 mph and eating it. I almost doubt my ability to stay calm and deal with a flat.

Somehow, even though I've fallen off a horse at least 5 times (with a few somewhat gruesome results), the idea of crashing my bike seems so much worse. This is admitted totally illogical because bikes are lower to the ground, not living, infinitely lighter, and probably safer. Anyway, to feel better, I'm going to study this video endlessly:

Ugh. They make it look SO easy. This video is LITERALLY 2:45 long. If I could change a tire in 2:45 I'd be golden. Although, that's not at all realistic, I'd still like to be able to do it relatively quickly so I could potentially get back in the race.