Biking the Katy trail

ME and my mom were considering biking the trail from St. Louis to Clinton. Is it safe for a
mother and a son to ride it and camp outside? Is it hard to bike while carrying supplies such
as a tent, clothes and some water and snacks? Is it better to camp outside or to stay in
motels along the way? How long does it take to do a round trip?

If you stay in designated campgrounds, B&Bs or motels you are as safe as this world gets. The amount of gear you carry has a huge bearing on the difficulty of the ride. Don't try to carry enough snacks etc. to do the whole trip, just what will get you comfortably to the next stop or store. Unless you are avid campers and experienced cyclists it is far easier to stay in B&Bs. It drastically reduces your load and makes for more relaxed riding, but that is a very subjective choice. As to time, how much are you training for this ride? I wouldn't try to do more in a day than double what you do in a two hour training ride. If you ride 20 miles in a two hour training ride with no gear three times a week or more, for more than 4 weeks, then top your days on the trail at 40. You'll have to adjust that some to fit the towns but even 40 miles day after day with gear is a ride for most people without a lot of experience and even for some WITH a lot of experience. And 4 weeks of training is NOT a lot of experience. But definitely do it! You'll be surprised what you feel like AFTER you accomplish a trip like this. Enjoy your ride.

For your first end-to-end on the Katy, I'd suggest staying in b&b's. Keep your load as light as possible. When I did my trip, I packed one change of clothes to wear every evening, and washed out my riding clothes in the shower every other night. Don't pack too much food. I brought beef jerky and fruit snacks, and I also kept a granola bar with me every day in case there was no place open for supper in the town I was staying in that night. I restocked as needed as I rode through towns. Your number one priority is to stay hydrated. I drank only water my first two days (and not much of it) and I felt terrible. My third day I switched to gatorade and drank constantly, and I felt like a million bucks. Gatorade replaces the electrolytes you lose when you sweat, so it keeps you balanced....water doesn't. I never was a big Camelbak fan until I took my trip, but I'd highly suggest you and your mother purchase a couple because they allow you to drink a lot more consistently than you would with a water bottle.
As far as length of time, I allowed myself six days one-way from Clinton to St. Charles since I wasn't in very good shape and I wanted time to explore the towns. I could have very easily finished in five, though. It seemed to me that it was a very slow and steady uphill ride from Clinton all the way to Boonville, so if you do a round trip, I wouldn't try to do your longest day on that stretch of trail. Once I reached Boonville, it was easy as pie the rest of the way to St. Charles. For your first time, I'd suggest 10 days for a round trip. If you are in decent shape, you can do it faster than that, but since it's your first time you'll have a little extra time built in for sightseeing and resting your sore butt!

Food shouldn't be an issue if you're biking. Utilize some of the existing eating establishments. There are some gaps where you won't see many but it cuts down on the amount of food you need to carry. Also try freezer bag cooking. It's light, easy, and good. Just do a web search on freezer bag cooking, you'll find some great sites. Camping is the way to go but this, like riding, takes practice. Pack all you think you'll need and then go for a long ride. You'll be amazed at what you think isn't worth carrying.