Mayority of linux distributions contains a /etc/profile.d which contain a few bash script that are executed on bash login
you could add the following file there, the name is not important just need to end in .sh
e.g. /etc/profile.d/PS1-git.sh
In order to add the file to /etc/profile.d
you probably would need root access.
# Define here your own colors.
# @see https://en.wikipedia.org/wiki/ANSI_escape_code#Colors
USER_COLOR='32'
ROOT_COLOR='31'
GITCOLOR='33'