Non-Gaussianity of the local type will be particularly well constrained by large scale structure through measurements of the power spectra of collapsed objects. Motivated by properties of early universe scenarios that produce observationally large local non-Gaussianity, we suggest a generalized local ansatz and perform N-body simulations to determine the signatures in the bias of dark matter halos. The ansatz introduces two bispectral indices that characterize how the local non-Gaussianity changes with scale and these generate two new signals in the bias. While analytic predictions agree qualitatively with the simulations, we find numerically a stronger observational signal than expected, which suggests that a better analytic understanding is needed to fully explain the consequences of primordial non-Gaussianity.