I know that given $\phi: X \to \mathbb{P}^n$ a rational map, where $X$ is for example a projective curve, $\phi$ can always be resolved as a sequence of blowups. Now I consider the map $\phi$ that associates to the stable extension of the type $0 \to \mathcal{O}_X \to F \to L \to 0$ the bundle $F$. So, $\phi: \mathbb{P}(Ext^1(L,\mathcal{O}_X)) \to SU_C(2,L)$, where $SU_C(2,L)$ is the moduli space of stable vector bundle of rank two and fixed determinant $L$ of odd degree. I know that the space where this map is not defined is the secant variety.
Now, for an opportune degree (greater than 3) I have also the following embedding $\psi: X \to $. How can I resolve the rational map $\phi$ as a sequence of blowups, also thanks to this embedding?