Try going up to US 84 or Alabama Hwy 10 (up US 231 from Dothan) into Mississippi. Both are good roads and I really like 10 but it take you to the interstate for a little bit as there is not a lot of options from Meridian to the west side of Jackson. Then up US 49 (84 will hit it at Collins, AL 10 goes to Meridian and you will hit I-20 then to Jackson) toward Yazoo City. Here you are aiming to cross the Mississippi river at US 84 near Greenville. You can either cut across Miss. Hwy 12 to Hwy 1 or for a better motorcycle road look for Hwy 433 at Bentonia. Take a left and you will find a good curvy road through the hills next to the delta. At the stop sign for Hwy 3, go straight across, this is the Satartia road and it is a country road through the delta. When you come to the next stop sign you are in Holly Bluff, take a left which will be Hwy 16 into Rolling Fork. At US 61 take a left then a right on Hwy 14 which will take you to Hwy 1. A right on this will go toward Greenville. Just before it look for Hwy 454, look for the casino sign as the highway is poorly marked, take a left and it will take you to US 84 just east of the River. Cross the river on the new bridge into Arkansas. This will merge into US 65, watch out for the transition from old pavement to new. There is a very hard bump there that is hard to see until you hit it. That will take you into Little Rock.
Have fun, stay safe.