Você pode especificar explicitamente que deseja iniciar um shell de login interativo:
ssh user@host bash --login -i
A "função" de ~/.profile
(ou ~. / bash_profile) e .bashrc
para ssh tem alguns outros arquivos,
(veja man ssh
para detalhes):
~/.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.