There should be some sort of conversion tool available in ArcView that can help users to convert various image formats to ArcView/ArcGIS specific formats, or between them. These special formats are generally used to save map and other GIS data. So perhaps this is a way how to achieve bpw to bil conversion.
Convert ArcView world file for bip or bmp images to ArcView band interleaved by line image format.
We found one software available in the database for this conversion.
Microsoft Windows software - convert bpw to bil on Windows
A GIS application used to work with geographic data
Convert from bpw file format
The table with program actions contains information about what each program is capable of doing with their files. This may be a good pointer for further searches for certain file conversions and help you find the converter you are looking for if our search result is insufficient for you. However, it is far from perfect and may sometimes show results which are not really usable because of the nature of the software handles the files. So a conversion that appears as possible, just because of matched actions, may in fact not be possible.