Hi
Quick and dirty:
Play the subtitled DVD in a DVD player, with S-Video or Component out being routed inro a Beta recorder.
(Assuming you’ve got an NTSC DVD).
If the movie artifacts are too noticeable, you could burn a new DVD from your DVD SP project with no video, just subtitles (replace all the movie tracks with black slugs) and capture a DVD play-out of subtitles only into your computer, and then after checking for sync slippage, screen-mode composite, or matte, or wipe the subtitles over your edit timeline, render and playout to Beta.
Proper full-res way I suppose is to make graphics of the sub-titles then rebuild your project painstakingly 😉