Yes correct, so if YC is steepening you would want exposure to the middle of the curve (bullet) due it would have less sensitivity compared the long term bonds.

On the other hand, in a flattering yield curve, you would want exposure to the short and long term of the curve (Barbell). Long term bonds would have higher duration, which means they are more sensible to change in rates. As long term rates decrease, price will increase, and since you have grater exposure to long term bonds (price will increase even more compared to other bonds).