Some people catch the entrepreneurial bur earlier, some develop it over time. No matter what the business, you will make mistakes, so the earlier you start, the more you can learn. Your success is determined by how much you can learn from your mistakes.
You can start part-time if you have a day job, but getting started is imperative. You can start a web development business on the side. The only thing that requires a schedule is meeting up with clients, but other than that you can work around your free time, evenings, weekends or whenever you catch a break.