Embird embroidery software supports even some older formats like BMC, so is probably your best bet to convert these files to Tajima DST.
Convert Embroidery graphic file to Tajima Embroidery format.
We found 2 software records in the database related to .bmc to .dst file format conversion.
Microsoft Windows software - convert bmc to dst on Windows
Popular embroidery design and printing software
Convert from bmc 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 bmc to dst. 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.
Multiplatform software - convert bmc to dst on any platform
Advanced version of the popular Embroidermodder