Programs like mapc2mapc are specially designed to manipulate and convert various geographical maps or charts, including .bsb (MapInfo) and .kap (Maptech) files. Other than that, you would have to use some common exchange format as middle step to achieve this conversion.
Convert MapInfo sea chart to Maptech BSB map.
We have found one software suitable in our database for this conversion.
Microsoft Windows software - convert bsb to kap on Windows
A digital map conversion software
Convert from bsb 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.