where to place universal bootstrapping code

All my scripts depend on some env vars & shell functions that effectively form a library.

Is there a system-wide place where such bootstrapping code could be placed so it's included in every shell session, regardless if it's running in a non-interactive script or user-facing shell? Eg I'd like to have following function definition to be globally available to be invoked on-demand:

function bootstrap() {
    source "some-library.sh"
}

Minimally this should work for scripts ran by one specific user, but would prefer a solution that also extends to scripts executed by root.

So far I've tried /etc/profile & /etc/bash.bashr but no joy.

both /etc/{profile,bash.bashrc} had something similar:

_inittest_first() {
    echo this is imported from /etc/profile;
}
export -f _inittest_first

I presume export is not working due to dash being involved somewhere inbetween, as explained here