Show me the machine! (Or at least, show me MY gear!)
Yes, you will probably have a big red toolbox on wheels. And most mechanics are responsible for buying their own tools up to a certain size. Beyond that, most shops provide those big sockets (try 2 3/4", for example!), high-powered air tools, and torque wrenches capable of supplying the several thousand PSI required by some hydraulic cylinders.
You'll also find that a laptop computer is a pretty valuable item in your toolbox, because more and more buses are equipped with computerized diagnostic systems that allow mechanics like you to do the work without having to tear the machines apart.
By the way, if you'd like to see what you'll be working on, look at "Show Me The Machine" in the different driver/operator sections of this site.