A resposta à sua pergunta pode ser encontrada na seção INVOCATION
de man bash
.
Aqui está um trecho relevante:
When bash is invoked as an interactive login shell, or as a non-inter-
active shell with the --login option, it first reads and executes com-
mands from the file /etc/profile, if that file exists. After reading
that file, it looks for ~/.bash_profile, ~/.bash_login, and ~/.profile,
in that order, and reads and executes commands from the first one that
exists and is readable. The --noprofile option may be used when the
shell is started to inhibit this behavior.
When a login shell exits, bash reads and executes commands from the
file ~/.bash_logout, if it exists.
When an interactive shell that is not a login shell is started, bash
reads and executes commands from ~/.bashrc, if that file exists. This
may be inhibited by using the --norc option. The --rcfile file option
will force bash to read and execute commands from file instead of
~/.bashrc.
When bash is started non-interactively, to run a shell script, for
example, it looks for the variable BASH_ENV in the environment, expands
its value if it appears there, and uses the expanded value as the name
of a file to read and execute. Bash behaves as if the following com-
mand were executed:
if [ -n "$BASH_ENV" ]; then . "$BASH_ENV"; fi
but the value of the PATH variable is not used to search for the file
name.
Há ainda mais na man page, eu recomendo que você leia.