arcpy.env.resample = "BILINEAR"
arcpy.Resample_management(input, output, "#", "BILINEAR")
No actual solution yet, but an acknowledgement of a bug. Progress!
Recent email from Tech Support:
This is just an update that in short, confirms that this issue is reproducible in-house.
arcpy.ApplySymbologyFromLayer_management faces the same issues as the Apply Symbology From Layer (Data Management) tool. Items in the Symbology tab are applied, and some items from the Display tab (like transparency) are applied, but 'Resample during display using:' is not applied. Furthermore, using the tool or code, the 'Resample during display using:' parameter is reset to Nearest Neighbor if the raster was originally set to Bilinear Interpolation (and the .lyr was set to Bilinear Interpolation as well). This happens for some raster datasets (i.e. those produced from Kernel Density - Spatial Analyst). As a result of this ticket, the following bug has been logged:
[#NIM103676 Apply Symbology From Layer (Data Management) sets 'Resample during display using:' in the Display tab to Nearest Neighbor. ]