A sequence of $S_n$-representation $V_n$ is called representation (multiplicity) stable if after some $n$, the irreducible decomposition of $V_n$ stabilizes. In particular, Church, Ellenberg and Farb found that if we fix $a$ and $b$, then the space of diagonal harmonics $DH_n^{a,b}$ exhibits this behavior, and its dimension stabilizes to a polynomial in $n$ eventually. Building on this result, we use the Schedules Formula to get an explicit combinatorial polynomial for the dimension of the bigraded spaces $DH_n^{a,b}$ combinatorially. This derivation not only yields the dimension formula but also produces a new stability bound of $a + b$, which is conjectured to be sharp, and determines the exact degree of the dimension polynomial, which is also $a + b$.