Start time: 12:40 PM (CST) @ Bag End
Great East Road: 4 minutes
Brandywine Bridge: 17 minutes
West Gate of Bree: 32 minutes
South Gate of Bree: 38 minutes
Forsaken Inn: 50 minutes
Last Bridge: 81 Minutes
Ford of the Bruinen: 99 minutes
Gates of Imladris: 113 minutes
Bridge of Rivendell: 118 minutes
End Time: 2:38 PM (CST)
Just barely under two hours from Bag End to Rivendell.
In terms of in-game time, I started in the afternoon and ended up in Rivendell at a little past Dawn.