The best way to safely transport an alto sax is by carrying it in a carrying case or bag. There are dozens of options on the market when it comes to carrying case or bag for saxophones. Keep in mind that you need a harder carrying case/bag rather than softer one for maximum protection. You can take a look at a case like the Protec PB305CT Tenor Saxophone PRO PAC Case. It is a shock-absorbing, weather-resistant carrying case that is designed to offer maximum protection to your horn.