Thanks for posting and welcome to the board. Couple things:
You say you only took 3 levels of wizard, but one of the requirements for eldritch knight is the ability to cast 3rd-levels. Did your DM waive that for you?
Also, you don't need a bastard sword to use a hand for spellcasting or unarmed strikes. You don't drop a greatsword just because you momentarily use one hand for something else. And in the case of unarmed strikes, you can of course use feet, elbows, head-butts, etc.
About the only real reason to use a bastard sword instead of a greatsword is if you're going to use a shield or wield another weapon. Unfortunately, that does tend to make a katana-wielding character a suboptimal build.
You say you only took 3 levels of wizard, but one of the requirements for eldritch knight is the ability to cast 3rd-levels. Did your DM waive that for you?
Also, you don't need a bastard sword to use a hand for spellcasting or unarmed strikes. You don't drop a greatsword just because you momentarily use one hand for something else. And in the case of unarmed strikes, you can of course use feet, elbows, head-butts, etc.
About the only real reason to use a bastard sword instead of a greatsword is if you're going to use a shield or wield another weapon. Unfortunately, that does tend to make a katana-wielding character a suboptimal build.