I can't type a “b” when I'm in the command line

Inside the ssh session, start a cat command and see whether you can type b there. I'm almost sure it'll work, which means that it's your shell that decides not to act on b.

Assuming the default bash, you should check readline's configuration files: ~/.inputrc, /etc/inputrc, or the one referred by $INPUTRC. Chances are you'll find an accidental lone b on its own line (or something similar), instructing readline not to do anything upon encountering this character.

Update

Looks to me that the first three lines of your .inputrc are correct, it's the fourth line (bind TAB:menu-complete) causing the trouble. Change its first letter to anything else (e.g. find instead of bind) and then that letter (e.g. f) will misbehave. Apparently bind is not a recognized keyword in this context.