Personally, I didn’t get my license until I was 26. Before 19, I was worried about my temper leading to road rage, then I spent a few years in the Navy, which would make a car a waste since there is little parking for E4 and below, and I was away from land too much to get much use from a car.
This may sound crazy, but some video games actually help you get the basics. They teach you the dangers of excessive speed, and other things about how cars handle. By the time I actually got behind the wheel (in a snowy field), I already knew how to avoid giving it too much gas for the bad conditions that you likely will never see, and that the brake pedal stops the wheels but may not actually stop the car. Having a sense of how long it takes to stop and how hard you can turn the steering wheel before running into issues are also important things video games taught me.
If you can walk across the street without getting hit, you already have enough situational awareness to not cause an accident. Just avoid tailgating and you can also avoid accidents caused by others in front of you.
Running out of gas is unlikely unless you are totally oblivious. I drive 50–75 miles a day and a full tank lasts me about four days. Two fill-ups a week is enough for me, so it’s not an everyday thing. Cars have this nice little gauge that lets you know how much gas you have, and so long as you don’t let it get below ¼, running out of gas is nearly impossible; for most cars, that is enough for at least 50 miles, or for quite a while stuck in gridlock. The only times i have ever run out were when I was pushing my luck the day before payday and was too broke to comply with that ¼-tank rule. Unless you are poor enough to be eating nothing but Ramen noodles everyday, you can probably afford to keep enough in your tank to stay out of trouble.
Above all, remember that driving is safer than bicycling. You have managed to not get killed on your bike, so you should do just fine with four wheels and a ton of metal surrounding/protecting you.
Lastly, if you are not afraid, then there is something wrong. It’s the people who drive without fear that cause accidents. People like the street-racer who thinks that they won’t get killed doing 120 mph as they cut across three lanes, or the person who thinks nothing bad will happen if they take their hands of the wheel to apply makeup. Fear is healthy; it keeps you alert to danger and it’s easier to avoid danger that you are aware of than danger that is hidden. Just learn to use that fear constructively. My wife is always scared to death, and that makes her safer behind the wheel than I am (I am merely nervous behind the wheel).