The expense of traditional capture‐recapture methods, interest in less invasive survey methods, and the circumpolar decline of polar bear (Ursus maritimus) habitat require evaluation of alternative methods for monitoring polar bear populations. Aerial line transect distance sampling (DS) surveys are thought to be a promising monitoring tool. However, low densities and few observations during a survey can result in low precision, and logistical constraints such as heavy ice and fuel and safety limitations may restrict survey coverage. We used simulations to investigate the accuracy and precision of, DS for estimating polar bear abundance in sea ice habitats, using the Chukchi Sea subpopulation as an example. Simulation parameters were informed from a recent pilot survey. Predictions from a resource selection model were used for stratification, and we compared two ratio estimators to account for areas that cannot be sampled. The ratio estimator using predictions of resource selection by polar bears allowed for extrapolation beyond sampled areas and provided results with low bias and CVs ranging from 21% to 36% when abundance was >1,000. These techniques could be applied to other DS surveys to allocate effort and potentially extrapolate estimates to include portions of the landscape that are logistically impossible to survey.