Simple:

Use Find/Replace, with the string you want to count for both the Find and
Replace.

Cheers

Use the Edit>Replace feature

Type the word or phrase you want to find in the find what window and type ^&
in the replace with window.  Then press replace all.

Word will report the number of replacements made.  ^& instructs Word to
replace with the contents of the Find what window, so your document is
unchanged.