I prefer to convert the video into AVI, and burn the subs using VirtualDub and Lee Avery's Subtitler plugin. This completely avoids audio slippage, and produces GREAT quality. Most of all, you can see the actual results before committing machine time to do it.
Other options are:
Any Video Converter is what you are asking for, however you'll have to do some trial-and-error before getting it right. You only see the outcome after it has been done.
Movavi is another excellent video converter , very fast and resource-laden, which offers the possibility of burning subtitles, however I never tried it to do it.
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