Individual heterogeneity is an important source of variation in demand. Allowing for general heterogeneity is needed for correct welfare comparisons. We consider general heterogeneous demand where preferences and linear budget sets are statistically independent. Only the marginal distribution of demand for each price and income is identified from cross‐section data where only one price and income is observed for each individual. Thus, objects that depend on varying price and/or income for an individual are not generally identified, including average exact consumer surplus. We use bounds on income effects to derive relatively simple bounds on the average surplus, including for discrete/continuous choice. We also sketch an approach to bounding surplus that does not use income effect bounds. We apply the results to gasoline demand. We find tight bounds for average surplus in this application, but wider bounds for average deadweight loss.