Try: set bind-tty-special-chars Off in your .inputrc, before you do the bind on C-z. The readline man page is a little misleading: bind-tty-special-char

Try: set bind-tty-special-chars Off in your .inputrc, before you do the bind on C-z. The readline man page is a little misleading: bind-tty-special-chars (On) If set to On, readline attempts to bind the control characters treated specially by the kernel's terminal driver to their readline equivalents. Disabling it doesn't actually stop readline from binding those control characters. It just enables you to override those default readline binds. If the variable is set to On (the default), that's not possible.