Just as you might practice various run throughs or rounds focusing on frame, timing, various aspects of technique, etc, do some rounds thinking about facial (and other) expression. Plan what you want to project (happy, sultry, serious, playful, telling a story, whatever), and practice projecting that through the whole dance regardless of how well or badly it goes.
Agree on spending some of your lesson times (when you might otherwise be making thinking faces, or oops faces, for example while learning new material) working on smiling and not letting your face betray the thinking or oops or frustration.
If you do any social dancing, this is another place to practice looking pleasant and unperturbed, regardless of what happens on the floor. Not necessarily going for a performance face, but not showing mistakes, etc. If you can look like you're having a good time despite the bad traffic on the floor, getting bumped into, you have no idea what that guy just tried to lead you through, and oh, by the way he's off time and gripping your hand too tightly ... you're on your way to not making bad faces on mistakes in routines with your pros. You can watch female pros at social dances to see how they do this. In order to keep students comfortable, I'm sure many of them spend a fair bit of time acting like they're having a bit more fun than they actually are. (I'm not saying they don't enjoy dancing with their students, just that some make it look like they're enjoying every minute, when clearly not every minute is equally enjoyable!)
In other words, it's just another skill to be practiced. You're lucky that you have some good natural expression to fall back on. Now you just need to work on your filter, and practice alternatives so you can short circuit the natural oops/frustrated/concentrating faces, and show something else during those times.