The default login shell for AIX is not bash - it is ksh/posix. The reason why the "up" arrow isn't working is because KSH is set to "vi" mode (bash can do this too). You want "emacs" mode:
set -o emacs
The .bashrc equivalent is .profile. You can put the above in there to change it permanently. AIX actually gives you two versions of KSH - ksh88 (default) and ksh93. The latter supports .kshrc as well
You can also install bash (and vim, nano etc) on AIX using an RPM available from one of the publicly available repositories. I wouldn't recommend installing yum.