by the way, I changed in the sketch the symbol TILDE with the sign'-',in order to try to change the speed of the UART- I don't have the symbol TILDE- and it worked: if I send '-1' it answer 'Speed set to 115200' or if I type '--' it answer 'Sending bridge's shutdown command')
You may want to rethink that. The idea is that it is not a character that is normally used when talking to Linux, so that it can act as an escape character to talk to the code in the sketch. Normally, anything you send to the sketch via the USB serial port is passed through to Linux. Sending this character means that the next character should be processed by the sketch.
You can still use '-' as your escape character, but that means that any time you want to send '-' to Linux (which is often used for command line parameters) you will need to send '--' instead. Some Linux command line switches use '--' so you will have to double both of them and send '----'.
It's good that you are able to send the change serial port speed commands, as that shows the sketch is working and the computer to AVR processor communications are working. That command changes the speed of the communications between the AVR processor and the Linux system. The Linux side is always using 250000 baud (unless you've changed it, and given that you haven't been able to log in yet, it's safe to assume it hasn't been changed.) So, either don't try to change the speed, or only use the '2' speed option. If you tried changing the speed, perhaps to 115200 to match the Serial Monitor setting, that will prevent sending/receiving anything from the Linux system, and could explain why you aren't seeing anything?
If I send the command for the bridge shutdown, what should I see?
Normally, the Linux serial port that is connected to the AVR processor through shield connector pins 0 and 1 is running a command shell and is acting as the console sending log output. The latter is what sends the log messages you should be seeing at startup, while the former allows you to send commands to Linux once it's booted up. The command shell is also what allows the Bridge library to work. When you call Bridge.begin() in a sketch, the sketch sends a series of commands to the Linux port to launch a Python script which handles the Linux side of the communications protocol. While that script is running, the Linux serial port is tied to the script, and cannot process any shell commands. Sending the bridge shutdown command tells the Python script to exit and return to the command shell.
So, since you have just started (or are starting up the Yun) and haven't called Bridge.begin() from your sketch code, the Bridge is not running. Therefore, sending the bridge shutdown command should have no effect. (Although it may leave some garbage characters in the command shell's input buffer, causing the next command to not be understood.)