It turns out you can't. Nero Vision stupidly doesn't support subtitles even for DVD-Video.
I did find a method that might work to burn Subs into the video files in Nero easier though, if you want to try. The idea is that Nero by default uses it's own built-in decoders to transcode video from whatever format it's in to MPEG-2 for the DVD. If you disable the Nero decoders though, it will try to use the ones built-in on your system (which would probably be FFDSHOW). Since FFDSHOW supports Subtitles, it'll load and play them back during the transcoding, which will "burn" the subs into your video.
Here's how (I have NOT tested this):
1. Set up your system so FFDSHOW handles playback of the video file you want to burn, and displays the subtitles correctly when you play it back. You want FFDSHOW to have the subtitle support enabled by default (so that you don't need to turn it on once Nero starts it up).
2. Then, find the file C:\Program Files\Common Files\Ahead\DSFilter\NeVideo.ax and rename it to NeVideo.bak
3. Attempt to burn your video file as normal. You should see FFDSHOW's icons load in the Notification Area while Nero is transcoding the video.
4. That's it.