The are 7 different ways across 3 unique modes of transportation to help you travel from Baton Rouge to Allen. If you're only considering the price, you should check out the bus out of Baton Rouge towards Dallas, as it is the cheapest to Allen. It's common to find tickets for as low as $44. Greyhound operates from Baton Rouge to Allen, so you book your trip with them! Book as soon as you can, as there may be limited availability.
On your trip from Baton Rouge to Allen, it is best to book as soon as possible. It won't necessarily help reduce your price by a large amount, but will ensure that you have a spot on the bus or train.