I think my main issue was the lack of quotes around my command arguments. Also, thanks to @Mark Setchell I realized I should be using OUTPUT_VARIABLE in lieu of OUTPUT
At any rate, here is the answer I arrived at:
execute_process (
COMMAND bash -c "date +'%F %T'"
OUTPUT_VARIABLE outVar
)
This stores the output of the bash command into the variable outVar
file(WRITE "datestamp" "${outVar}")
And this writes the contents of outVar to a file called “datestamp”.