You need to learn a shot that checks up faster. Simple solution, but it takes lots of practice.
The goal is to add a lot of backspin—that way, you can hit a powerful enough shot to clear the bunker, but stop the ball before it rolls off the green.
Start with your sand wedge. Open the club face to add loft. Like, really open it, not just a fraction. Adjust the angle of your stance so that the leading edge of the club is once again aiming at the target. Re-grip the club after you're in this new position (otherwise your hands are going to go right back to their original position when you swing).
When you swing the club, swing it as hard as you can. BUT, adjust the power via the distance of your backswing. Follow through, so that your backswing is about 25% of your swing, and your follow-through is 75%. This aggressive swing will add a lot of power into spinning the ball without sending it into the parking lot.
It's hard, but once you learn it, it adds so much versatility to your game.