Regretfully I don't have an installed version of 6.34 available to me right now, but if you upgrade to 6.35 (the latest version), there is an option located at mIRC Options (Alt+o) -> Display -> Options
The option is called Editbox lines:
and has a dropdown box with the options of Single, Multiple, Automatic.
It looks to me like your editbox line (typing bar as you called it) is set for the equivalent of Multiple, and you want Single.
Personally, I love the Automatic setting, as the editbox increases in height as you type, rather than having the text scroll off the left hand side (as in previous versions).