Hello Kyle,
Sorry if this reply is too late to help.
If you capture the video and then compress it to MPEG-2 for DVD, the captions will be lost. This is because MPEG-2 for DVD is 720x480 and doesn't include the line 21 area where closed caption data is stored for analog video like BetaSP. The captions are stored separately as metadata on the disc, so they need to be extracted and converted using a special process.
The easiest option would be to use a set-top DVD recorder (like a VCR that records on DVDs). These internally convert the analog line 21 caption data into DVD closed captions when recording. If you need to have custom menus or chapters, you could then extract the MPEG-2 (which will include the caption metadata) off that DVD, and re-author a new DVD without re-compressing the video.
Another option would be to send the tapes to a caption service company which can extract the closed caption data and e-mail you a .SCC file, which you can bring into Adobe Encore or another professional DVD authoring program to author a DVD with closed captions.
If closed captioning is something you deal with a lot, you might want to consider purchasing software so that you can author & convert captions and subtitles on your own system.
Jason Livingston
CPC Closed Captioning