General :: Extract The First Word Following A String?

I need a bash script that can read a file, say example.txt search for the string "This is my example string" and save whatever word/number comes immediately after it to a variable, var.

Example:
blah blah
blah This is my example string extracthere is a very nice word.
blah blah

There are two constraints:1. This needs to assume as little as possible about the nature of the known string "This is my example string" and the word that follows it. I am trying to keep my code adaptable.2. Speed is valuable. This shell will be executed dozens if not hundreds of times so speed is very desirable. I thought I read that some commands are faster than others.