If we take that same pattern of half notes alternating between the bass and snare, and sart it on the second eighth note of the bar in stead of the first, it looks like this.
If we start on the third eight note, we get this.
And the only permutation left is to start on the fourth eight note.
I've found that by putting these backbeats in different places, I hear the bell pattern itself in new ways. This gives me a lot more liberty in trying to play new things. Again, it's very important that you keep the pulse with your left foot on the hihat. Otherwise you can lose track of where the one is. You want to practice these patterns until the backbeat pattern is strong and steady so that a listener might hear that as the meter, but you must also keep track of the original meter and maintain the bell pattern in your right hand.
Have fun.