Whilst probably not optimal and the result will be poor, it might be still possible to use one of the digitizing solutions like the Janome Digitalizer Pro program which is designed to make embroidery designs even from raster (bitmap) images instead of vector graphics.
Convert Standard Windows bitmap image to Brother Embroidery file format.
We have found 3 software records in our database eligible for .bmp to .pes file format conversion.
Microsoft Windows software - convert bmp to pes on Windows
An embroidery design tool from Janome
Convert from bmp file format
The tables with software actions are a good pointer for what a certain program does with various file types and often may give users a good hint how to perform certain file conversion, for example the above-mentioned bmp to pes. However, it is not perfect and sometimes can show results which are not really usable because of how certain programs work with files and the possible conversion is thus actually not possible at all.
An embroidery designs manager
Multiplatform software - convert bmp to pes on any platform
An embroidery digitizer