You can append to .bash_history immediately, and thus make the items available in any other open shells immediately as well. This is supported natively. Search for `shopt -s histappend`.
Also I just don't trust bash to actually keep my history, no matter what I do with HISTSIZE and HISTFILESIZE.
I have about a half dozen terminals open. I want to have the current shell's history seem consistent within any shell, but I want ^R in any NEW terminal to include all the commands entered in any terminal.
shopt -s histappend
HISTCONTROL=ignoredups:ignorespace
# append to bash history Right Now
export PROMPT_COMMAND="history -a"
Besides, since you load the HISTFILE at startup, you'll append your whole history (file+session) to the HISTFILE each time you exit a shell, so either it will grow very large quickly, or you set HISTFILESIZE to limit it but as a consequence you'll lose entries (and unfortunately not the oldest).
The option "only append the session entries typed in this session", while still using the whole history (file+session) for searching, is missing, as far as I know.