Let's say you have a variable in bash that already contains values.

foo="Hello World"

This works well if you don't need to use sed and regular expressions.

foo="${foo/World/Earth}"

This works well if you want to use a regular expression in the replacement. Ensure you double quote your variable ("$foo" in this example). This Unix and Linux Stack Exchange article explains the reasoning for this.

foo=$( echo "$foo" | sed "s|World|Earth|" )

Or, sed and <<< can be used to replace values in the variable. In this example, the word World is replaced with the word Earth.

foo=$( sed "s|World|Earth|" <<< "$foo" )

Printing the variable will now print the following.

Hello Earth