You may explicitly specify that you want to start an interactive login shell:
ssh user@host bash --login -i
The "role" of ~/.profile
(or ~./bash_profile) and .bashrc
for ssh have some other files, (see man ssh
for details):
~/.ssh/environment
Contains additional definitions for environment variables; see ENVIRONMENT, above.
~/.ssh/rc
Commands in this file are executed by ssh when the user logs in, just before the user's shell (or command) is started. See the sshd(8) manual page for more information.