Enable feature with this option in .tmux.conf:
set -g @resurrect-save-bash-history 'on'
Bash history for individual panes will now be saved and restored. Due to
technical limitations, this only works for panes which have no program running
in foreground when saving. tmux-resurrect will send history write command to
each such pane. To prevent these commands from being added to history
themselves, add HISTCONTROL=ignoreboth to your .bashrc
(this is set by default in Ubuntu).