bash profile is not loaded while running a remote script with ssh

Situation:

There is a bash script called hello.sh on HOST-A. This script uses some environment variables that are available on HOST-A. I am executing this script from HOST-B.

When I execute the hello.sh locally from HOST-A it sees the environment variables.
But if I run the script from HOST-B using ssh, the script does not see the environment variables.

Environment:

• HOST-A and HOST-B are docker containers based on alpine:3.17.3.

• Port 13012 is the docker port of HOST-A (13012:22)
• Port 13022 is the docker port of HOST-B (13022:22)

Test, that works like a charm:

• When I log in to HOST-A using docker exec -it HOST-A /bin/bash then the script sees the environment variables.
• When I log in to HOST-A using ssh -p 13012 root@localhost then the script sees the environment variables. Port 13012 is the SSH port of the HOST-A that Docker maps to the host machine.
• When I log in to HOST-B, then ssh HOST-A, then run the script, the script sees the environment variables. Here I test the ssh connection between the hosts in Docker too.

Issue:

The bash profile is not set when I run the script remotely from HOST-B using the

[root@HOST-B]# sshpass -p "password" \
                  ssh -oStrictHostKeyChecking=no root@HOST-A 'bash -s < /hello.sh param'

When I try to run the script from the docker host machine using sshpass -p "password" ssh -p 13012 -oStrictHostKeyChecking=no "root@localhost" 'bash -s < /hello.sh param' then it also does not work, the bash profile is not set.

Warning:
The param must be a variable: $param

I think that the issue is that the bash profile is not set when I connect with ssh.

What I have tried but did not work:

I created .bash_profile, .bashrc, and .profile. They have exactly the same content:

# pwd
/root

# ls -all
-rw-r--r--    1 root     root            86 May 14 23:52 .bash_profile
-rw-r--r--    1 root     root            86 May 14 22:38 .bashrc
-rw-r--r--    1 root     root            86 May 14 22:52 .profile

How to set bash profile properly for ssh remote execution in alpine Linux?

☆☆☆ UPDATE ☆☆☆

If I source the .bashrc in the hello.sh then everything works fine. But this is a hack, looks really bad.

source ~/.bashrc

To have .bash_profile being processed, you need to specify the -l option when invoking bash. This makes bash a login shell. In this case, the other login-startup-files are processed too (as specified in the section INVOCATION of the bash man-page), for instance /etc/profile.