From Baton Rouge, LA bus to Jackson, MS then bus to Monroe, MS. 7 h 29 min $75. From Baton Rouge, LA bus to New Orleans Union Passenger Terminal Amtrak, train to Jackson, MS, then bus to Monroe, LA. 9 h 33 min $120. From Baton Rouge drive to Monroe. 4 h $22. From Baton Rouge taxi to Baton Rouge airport, fly to Monroe airport, then taxi to Monroe. 3 h 47 min $646.