When traveling with your instrument there are some rules I like to follow to insure my instrument is protected and safe.
Just walking with your instrument can be an adventure, especially when you are new to the feel, weight, size, etc. of your instrument. Keeping your instrument on your back (with backpack straps) helps keep it out of the way of bumping into walls, doorways, people or anything else you might find your instrument trying to attack! :-) Using a shoulder strap is another good way to keep your instrument out of harms way. A cross-body strap is also a good idea. Using your hands to carry your instrument/case works, but the chances of hitting the nose (scroll part of instrument) into something does go up quite a bit. Use good common sense and keep it safe!
Don't place your instrument in the 'trunk' if your trunk is separate from the rest of the cars heating and cooling. Keeping your instrument in the same temperature you are comfortable in is the best way to make sure your instrument is safe. Please don't leave your instrument in a vehicle that does not have a shaded spot with a temperature condition that you would be happy to sit in for 30 minutes without added air-conditioning or heat. Instruments never go in a 'trunk' or other place that is not temperature controlled.
Okay, so you want to ride the bus to school and back home. No worries (she said nervously!). Riding a bus is tricky with an instrument.
If you are a violinist or violist you would ideally sit in a seat with your backpack at your side and your violin/viola in-between your legs planted on the floor of the bus. If you are a cello player you would have your backpack on your lap with your cello safely secured between you (sitting towards the isle) and the cello next to the window resting on the seat. If you are a bass player -- your parents need to transport you and your bass, or take up an entire seat, just for the bass.
I cannot speak for our schools bus company and their policies, but I can tell you that treating your instrument with care, space and secure placement is paramount to the well being of the instrument and yourself. I like to think of handling my instrument like I would an infant in a car seat -- take your time, secure placement (not bumping around and such) and most importantly -- not knocks into other items! Please remember that your instrument is made out of wood -- most of the parts are not even glued on, just held in place with pressure from the other parts! Easy goes it! I know you will do a great job protecting your instrument.
If you ride your bike to school, music lesson, friends house, etc. it is best to keep in secured on a backpack strap system. You may need to make alterations to fit your instrument safely behind you and still avoid it knocking into your bike helmet. Sometimes a cross strap is the best way to go. Experiment with straps to see what works best for you, your bike and the precious noggin on top of your shoulders.
Violins and violas are ALWAYS a carry-on! You can call ahead when or shortly after purchasing your tickets to inform the airline you will have a carry-on violin/viola. Putting your instrument in the 'belly' of the plane almost always ends in a beautiful instrument becoming a nice pile of kindling for the fire!
Cellos do have travel cases designed to take the blunt force trauma of air travel. People have had success with the cases, they are pricey though. Traditionally musicians purchase a seat next to them for their cello. Please take the time to inquire with your chosen airline as to their policy. Checking your cello without a special case is a recipe for disaster.
Basses - just don't do it! Think of your bass like a piano -- when you get to where you are going, rent one :-)
Train travel is pretty much self explanatory. Don't leave your instrument unattended and away from hot sun soaked windows. Please remember that if a good thief if looking to score a fine instrument they don't know if you have a multi-million dollar instrument in your case or a student level.
Just don't do it! Water is poison to a wood instrument!