Yes, you can bring a bike with you on trains and buses. Buses are equipped with racks in the front of the vehicle (buses can only accommodate two bikes at any time). Trains have luggage/handicap space in each end of rail cars and in the center of the car where you can stand with your bike.
As a bonus, many MARTA stations also have bike racks inside the station, so you can securely leave your bike inside the fare gates. Bike repair kiosks are also available in some stations. For more information, see MARTA’s bicycle guidelines.