I've thru-hiked the Batona Trail 92 times and I can tell you that people ride mountain bikes on it, dirt bikes, horses and even vehicles in some sections. I've lost count of how many times I've stepped in horse s*#t hiking the Batona Trail at night near the Carranza Memorial. I wonder how the owners of those horses would feel if I moved my bowels all over the ground where they walk?
There are hundreds of miles of dirt roads and fire lines you can explore in the pines on a mountain bike, however, if you do decide to bike the Batona Trail, let me give you two bits of advice that will keep you in good stead with the hikers.
1) If you're approaching hikers from the front, be courteous and yield to them. If you come barreling down on them aggressively with a posture of, "Get out of my way or get run over," you may annoy them to the point where they phone the Park Police and complain.
2) If you're approaching somebody from behind, gently start clapping your hands, softly whistle or say "hello" when you get within 50 yards of them to alert them of your presence. Don't wait and shout, "EXCUSE ME!" when you're two feet behind them. Nobody likes being startled like that.