Keep in mind that the Natchez Trace is 45mph the ENTIRE length and it is patrolled. Since it is a Fed offense, it is more expensive than a typical state/municipal ticket. Unless you have the time for a leisurely drive down the trace, I would avoid it or just do a short section of it. It is not really anything special road wise, just wide sweepers and gentle rolling hills in the woods, much like many FMs in East Texas... but MUCH slower
There really isn't an exciting way to get across East Texas and Louisiana without losing a lot of time, so I just take the most direct route East. Once into Mississippi and Alabama, things get better. I generally loop around the North side of Birmingham and come into North Carolina near the Tennessee/NC border, which is close to the Cherohala Skyway and Deal's Gap. From there it is a short hop over to Cherokee, NC., and the start of the Southern end of the BRP. Most of the route below is highway speeds and not too indirect, so you can still make pretty good time. It is two long days for most people or three medium days. A long day for most people is 500-600 miles unless they are used to doing consecutive long days in the saddle. A medium day might be closer to 400 miles. From my place in Huntsville to Guntersville in NE Alabama was right at 760 miles. I ran it alone, in NASTY weather and fog and it took me about 18 hours.
When I made the trip, I typically ran US 190 to Jasper, Tx 63 to the border, and then La121/28 through Alexandria to Natchez. Then if I feel like it, I might run the Trace up to Jackson. You can get off the Trace and run MS 18 into Jackson as well if you want to run a quicker pace. If you are not used to knocking down long days in the saddle, Jackson will be a good stopping point for the day. It will be right around 400 miles, give or take a few.
From Jackson, head NE on MS 25 to Louisville and pick up MS 14 East. At the border, this becomes AL 32, which hits AL 17. Run 17 NE to Carrollton and pick up AL 86 running due East. At US 82, turn back NW a short bit to AL 159 and run North. At Fayette, head East on AL 43/18/69 to Jasper. Run 69 NE I-65, run up to Cullman, then head East on 69 To Guntersville. Guntersville is about 330 miles from Jackson. If you are making pretty good time, then you might want to press on to Rome, Ga., which is about another 100 miles. That last 100 miles is pretty cool though. You want to run AL 227 NE of town through the state park, then it turns back SE to AL 68 as Crossville. Run 68 East to AL 176 just on the other side of I-59 and turn North. About 10 miles up, 176 makes a hard right to the East and goes over to the edge of the Little River Canyon National Preserve. Then it follows the rim of the canyon NE to AL 35. This is a REALLY cool stretch of road and worth the short detour. Run AL 35 down across 68 to AL 9, then run 9 East to the border where it becomes GA 20. Run that on into Rome. That would make for about a 430 mile day from Jackson.
From Rome, head North on US 27 to GA 156. Run 156 NE to US 41, then pick up GA 225 North to US 76 and on into Chatsworth. Heading East out of Chatsworth, look for US 76, 52 or 2. Different maps show different numbers, but they are all the same road. It runs up into the mountains past the Fort Mountain State Park over to Ellijay. It is a great ride! At Ellijay, hop on GA 5 and run it NE to Blue Ridge. At Blue Ridge, it is decision time.
If you want to get to the BRP ASAP, then you will want to Stay on 5 just past town and look for Lakewood Hwy on the North side of the highway. That runs up to Mineral Bluff, where you can pick up Murphy Hwy and run that to the border and pick up NC 60 to US 64. Run 64 to US 19 and that will take you all the way into Cherokee where the BRP starts. It is about 180 miles from Rome.
HOWEVER....
You can also get there by way of some MUCH better roads!! Head North out of Blue Ridge on Blue Ridge Dr. to Copperhill, Tn. From there it becomes TN 68. Run TN 68 North all the way to Tellico Plains. This is a superb ride. I have done it numerous times. Stop in Tellico Plains and get gas. Then head East on TN 165 to NC 143. This is the Cherohala Skyway, 55 miles of motorcycle Nirvana. At the end of the Skyway, you can either peel off on on Joyce Kilmer Rd., to loop around the lake to US 129 or run 143 on into Robbinsville on 129. Either way, you will eventually head North on 129 to Deals Gap and the Crossroads of time. Run the gap a few times if you like so you can say you did it. Stop at the Crossroads of Time to take some pictures and get your T-shirt and stickers. Then head South on NC 28 all the way to Franklin. You will really like 28, especially the section just South of US 19!! Once in Franklin, you can stop for the night if you like. It will be about a 300 mile day if you do Deals Gap once. The Franklin Motel is a nice biker friendly place to stay with nice rooms and good rates. If you are still up for some easy highway miles, you can run on up US 441 to Cherokee and stay there for the night, but it will likely be more expensive. The start of the BRP is 33 miles from Franklin.
So that gets you to the start of the BRP. You can do it in two days if you are both up to doing 500-600 miles in a day. If you have not done that kind of distance in a while or are not used to riding such distances in a day, it might take more out of you than you think. With the two of you, you might want to consider doing three days, which is what I outlined above. Keep in mind, it is three days back as well unless you just slab it. Even if you slab on the interstates and major highways, you are still looking at two long days to get home assuming you start the ride home from the Western edge of the area.
The BRP is a great ride. Keep in mind that like the Natchez Trace it is also 45 mph and is patrolled. It is also a Fed ticket. There are a TON of great little paved backroads out in that area that are much less traveled and no less fun than Deals Gap and the BRP. If you want more info about those, let me know. To give you much more, I really would need to know what kind of time frame you are working with and how many miles you want to ride in a day. Bear in mind that a 250-300 mile day in the twisties of TN, GA, and NC is a LOT of riding in one day because of the amount of concentration it takes compared to something like riding the Twisted Sisters in one day.