I am writing a python script (Linux) that is adding some shell aliases (writes them to
os.system('/bin/bash -c source HOME/.bashrc')
What you want is not possible. A program (your script) cannot modify the environment of the caller (the shell you run it from).
Another approach which would allow you to do something close is to write it in terms of a bash function, which is run in the same process and can modify the caller. Note that sourcing during runtime can have possible negative side-effects depending on what the user has in their bashrc.