A bastard sword is about 4 feet in length, making it too large to use in one hand without special training; thus, it is an exotic weapon. A character can use a bastard sword two-handed as a martial weapon.
If a weapon is wielded two-handed as a martial weapon and one-handed with an exotic weapon proficiency, can I wield it one-handed without the exotic proficiency at a –4 penalty?
Note that normally you can't wield a two-handed weapon in one hand. A bastard sword is an exception to that rule that you can't wield a two-handed weapon in two hands, but you must have special training to use the bastard sword this way. Without that special training, wielding a bastard sword one-handed is as impossible as wielding a greatsword one-handed. (The same goes for other weapons with this one-handed exotic exception, such as the dwarven waraxe.)