How long would it take an experienced person to make a Bow?

If you have tools all ready made the job is quicker. A Bow isn't just a stick with a cord strung between the ends. The bow is specially shaped to taper and have rounded edges, there are also a couple of notches at each end. The bow is shaped not so much by carving but by scraping to shape tapers from center to the ends .

Using hand tools like planes and draw knives a bow can be roughed out in a matter of hours. However without such tools and using flint hand tools the job will take much longer especially if you consider the time it takes to make the flint tools and keep them sharp. Probably up to a week to 10 days if you include time spend foraging for raw materials such as a decent piece of straight grained ash, locating flint and preping these materials. If these materials are readily available and fabricated you can cut this time in half

If your talking about just the shaping of a bow from a stick once you have the material and tools it would probably take 1 to 2 days.

Again you have to consider the difference between using steel tools vs flint