Picard rank jumps for K3 surfaces with bad reduction

Let $X$ be a K3 surface over a number field. We prove that $X$ has infinitely many specializations where its Picard rank jumps, hence extending our previous work with Shankar, Shankar and Tang to the case where $X$ has bad reduction. We prove a similar result for generically ordinary nonisotrivial families of K3 surfaces over curves over ${\overline{\mathbb{𝔽}}}_p$ which extends previous work of Maulik, Shankar and Tang. As a consequence, we give a new proof of the ordinary Hecke orbit conjecture for orthogonal and unitary Shimura varieties.