String comparison in bash. [[: not found

I am trying to compare strings in bash. I already found an answer on how to do it on stackoverflow. In script I am trying, I am using the code submitted by Adam in the mentioned question:

#!/bin/bash
string='My string';

if [[ "$string" == *My* ]]
then
  echo "It's there!";
fi

needle="y s"
if [[ "$string" == *"$needle"* ]]; then
  echo "haystack '$string' contains needle '$needle'"
fi

I also tried approach from ubuntuforums that you can find in 2nd post

if [[ $var =~ regexp ]]; then
  #do something
fi

In both cases I receive error:

[[: not found

What am I doing wrong?