BINK videos, or rather videos compressed using the BINK codec, can be converter to several other formats including the MPEG-TV format (.ts). That can be done in almost any decent multimedia converter nowadays, but keep in mind that regardless of the output format, the quality won't be better than the original. In any case, bik to ts conversion is somewhat odd choice.
Older BINK videos, especially from computers, often lacked audio track that would saved in separated audio files. In this case you would have to use some video editing tool for importing the audio track to the video.