If your video has a closed caption file, select that in the subtitle dropdown, make sure the burned in option is not ticked, and add the file. They'll end up as subtitles that you can turn on or off in iTunes or iPhone/Apple TV/etc.
Instead of extracting an SRT file from the original DVD, search for the film title at www.allsubs.org
Always test the SRT file to be sure the timing is correct. To adjust the timing try "Sears". Any SRT hosted by allsubs has an advertising subtitle entry at the beginning and aniother at the end of the entries. You can erase the adverts and save in TextEdit, being sure not to "save as" a TXT file.