Append to the end of the file:
# System-wide bashrc file
if [ -f ~/.bashrc ]; then
source ~/.bashrc
fi
Add-Content -Path "C:\Program Files\Git\etc\bash.bashrc" -Value '# System-wide bashrc file'
Add-Content -Path "C:\Program Files\Git\etc\bash.bashrc" -Value 'if [ -f ~/.bashrc ]; then'
Add-Content -Path "C:\Program Files\Git\etc\bash.bashrc" -Value ' source ~/.bashrc'
Add-Content -Path "C:\Program Files\Git\etc\bash.bashrc" -Value 'fi'