Cheeger described in "Some examples of manifolds with nonnegative curvature" the connected sum $\mathbb C\mathbb P^n\#\overline{\mathbb C\mathbb P^n}$ as a biquotient: Take $(S^{2n-1}\times S^2)/S^1$, where $S^1$ is acting freely on $S^{2n-1}$ and by rotations on $S^2$. This is the associated bundle to the principal fibration $S^1\to S^{2n-1}\to\mathbb C\mathbb P^n$ with fiber $S^2$. See Example 3 of the paper mentioned above, why this is $\mathbb C\mathbb P^n\#\overline{\mathbb C\mathbb P^n}$.

Cheeger described in "Some examples of manifolds with nonnegative curvature" the connected sum $\mathbb C\mathbb P^n\#\overline{\mathbb C\mathbb P^n}$ as a biquotient: Take $(S^{2n-1}\times S^2)/S^1$, where $S^1$ is acting freely on $S^{2n-1}$ and by rotations on $S^2$. This is the associated bundle to the principal fibration $S^1\to S^{2n-1}\to\mathbb C\mathbb P^n$ with fiber $S^2$. See Example 3 in Cheeger's article, why the above quotient is $\mathbb C\mathbb P^n\#\overline{\mathbb C\mathbb P^n}$.