The domain walls between AB- and BA-stacked gapped bilayer graphene have garnered intense interest as they host topologically protected, valley-polarized transport channels. The introduction of a twist angle between the bilayers and the associated formation of a moiré pattern has been the dominant method used to study these topological channels, but heterostrain can also give rise to similar stacking domains and interfaces. Here, we theoretically study the electronic structure of a uniaxially heterostrained bilayer graphene. We discuss the formation and evolution of interface-localized channels in the one-dimensional moiré pattern that emerges due to the different stacking registries between the two layers. We find that a uniform heterostrain is not sufficient to create one-dimensional topological channels in biased bilayer graphene. Instead, using a simple model to account for the in-plane atomic reconstruction driven by the changing stacking registry, we show that the resulting expanded Bernal-stacked domains and sharper interfaces are required for robust topological interfaces to emerge. These states are highly localized in the AA- or SP-stacked interface regions and exhibit differences in their layer and sublattice distribution depending on the interface stacking. We conclude that heterostrain can be used as a mechanism to tune the presence and distribution of topological channels in gapped bilayer graphene systems, complementary to the field of twistronics.