Here's a map of the MCB: http://maps.nashville.gov/MusicCityBikeway/
You can see that the southern terminus of the MCB is Vaughns Gap and Highway 100. The Trace ends at HWY 100, 6.4 miles down the road from the MCB. This section of road can be congested and there are some bad rumble strips in certain places, but it is an easy connection nonetheless. Once you get to the MCB, your route will be well signed. It is a combination of greenways, bike lanes, and shared paths.
I hope this helps somebody plan a trip. Come visit us in Nashville!