How to convert .ogg files to .bik format.
Converting Ogg Vorbis Audio Files directly to Bink Video Files (.ogg to .bik conversion) should be possible, even though your options are quite limited.
It appears that your best option is using the Freemake Video Converter, which should be capable of converting .ogg to .bik.
Alternatively, you can try some available online conversion solutions, which claim to be capable of such conversions.