Perhaps you can differentiate between 'carry' and 'transport'. For Transport, gun unloaded in one saddle bag, (in a secured container (perhaps locked?)). Ammo secured in the other saddle bag, (in a secured container (perhaps locked)). Pretty sure you'd want to lock your saddle bags anyway. (I think this is per the Federal Transport Regs.)
For Carry. Open Carry or Concealed Carry?
There are probably others here who can better answer, and/or correct me if I am wrong.