Embroideries saved in one of the Brother formats (like .bdf) can be converted and saved to any of the other Brother formats, including the much more common PES format. Your best choice for this conversion would be to use the original Brother Embroidery software, for maximum compatibility between formats.
Convert Brother BES-100E Embroidery Software to Brother Embroidery file format.
We found one software available in the database for this conversion.
Microsoft Windows software - convert bdf to pes on Windows
An embroidery design software
Convert from bdf 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.