Yes, you can use substitutions and check against the original string:
if not x%str1:bcd=%==x%str1% echo It contains bcd
The %str1:bcd=% bit will replace a bcd in str1 with an empty string, making it different from the original.
If the original didn't contain a bcd string in it, the modified version will be identical.
Testing with the following script will show it in action:
@setlocal enableextensions enabledelayedexpansion
@echo off
set str1=%1
if not x%str1:bcd=%==x%str1% echo It contains bcd
endlocal
And the results of various runs:
c:\testarea> testprog hello
c:\testarea> testprog abcdef
It contains bcd
c:\testarea> testprog bcd
It contains bcd
A couple of notes:
The if statement is the meat of this solution, everything else is support stuff.
The x before the two sides of the equality is to ensure that the string bcd works okay. It also protects against certain "improper" starting characters.