Uh oh. You've got me out to hold forth.
As other folks have mentioned, a "bastard sword" is what was actually called a "longsword," and there's not much debate about this since period texts call it a "longsword" (langschwert). The D&D "long sword" is probably an arming sword, with extra flanges and crap in 3.5 or 4e art direction. Whatever.
Although, of course, an arming sword could be a hand-a-half sword, to the point where it could be considered a bastard sword... (you present the parallel situation for Japan below)
From one point of view, a katana is probably closer to an arming sword/D&D long sword than a longsword/D&D bastard sword . . . but there's a wrinkle. What we call a standard katana was actually standardized during the Tokugawa military government. Before (and during the early part) if the Tokugawa regime, swords tended to be bigger -- closer to "bastard sword" size. Some folks call these "tachi" to differentiate them, but the primary difference is really dimensions and how they are worn (blade down for tachi, up for katana -- in fact, the categories bleed together to the point where you can turn a tachi into a katana and vice versa by changing the way you wear it!) and in any event, these big swords were *also* called "katana," which is a very general term.
Much as in most times and places, the general term for sword was appropriated for describing whatever passed for a common military weapon in those times and places. Thus you end with situations where the term "rapier," used for swords generally in some times and places, gets appropriated for a certain type of thinnish blade, and the other "rapiers" become "longswords" because they resemble the longish, hilted weapons of older fencing manuals...
There's a TVTropes article that complains that people think every Japanese sword is a katana. The trouble is, well, for a long time they pretty much were. There's a huge procession of very similar curved swords for which it is not wrong to use the general term "katana," though it might get odd at the very big (giant swords were probably mostly given as gifts) and small (dagger-sized, tanto, shoto, etc.) ends of the scale. People like to drag out examples of tsurugi (straight swords) but they are barely remembered as anything other than ritual objects.
(And those straight ninja swords probably never existed.)
In reviewing for this little discussion, I learned a number of new words for swords. I didn't even know there was an "okatana" or however you want to render that.
Basically, this means that an Edo (Tokugawa government) period katana is like a D&D long sword, maybe with a feat that provides an extra bonus when the weapon is used two handed (as it usually was -- even dual-wielding patron saint Miyamoto Musashi usually kept both hands on *one* sword) while the weapons people like to call "tachi" could be treated as D&D bastard swords.
Lastly, you should remember the factor of size relative to the wielder. At 5'5" one poster is already a couple of inches taller than many period users. In a fantasy game where everybody's taller, their weapons are going to be built accordingly.
This raises the question: Is there any point to using a tachi one handed? Maybe if you're on a horse, or in another situation where you need your free hand to throw shuriken (taught in many schools to create space for a draw -- yep, more a samurai than ninja thing), grapple or do something else. Older schools (like the Tenshin Shoden Katori Shinto Ryu) conceivably taught the use of a larger sword in two-sword use back in the day, but this wasn't preferred unless maybe you had to cut down a lot of folks attacking from multiple angles (this is how Musashi apparently employed two swords against a bunch of swordsmen after killing their teenage leader in an ambu-er, "duel"). So taking it up a notch for D&D heroism it is not entirely out of the question, but for us mere mortals bereft of shields, we're probably okay with just the one large-ish sword.
I think you jumped a notch there. Although the tachi was bigger, it doesn't follow that tachis, in general, were much bigger. I'll argue that during the tachi to katana transition, they tended toward similarity in size.
If someone wants to purposefully emulate antique Japanese blades in the game, it's worth noting that not only where they larger, they were distinctly curved rather than compromise-curved as most katana, tended to lack chisel-points for stabbing, and generally had simple welded hilts rather than the more elaborate and decorative hilts associated with katana.
As for what to do with a katana or tachi in one hand, although two hands is more powerful and faster, one-handed allows a greater range of motion. I've seen numerous katana kata that show one-handed moves, as one might use in close quarters. That's probably a distinction of little consequence in-game, but there you go.
Why would a samurai purposefully use a tachi one-handed? While mounted, of course, but let me add to that, in conjunction with other weapons such as a lance, javelins, shuriken and shaken, and axes, which might also be used from horseback. On foot, two-handed would generally be preferred, as with Western swords.
just make a "proper" katana a "masterwork" weapon as they were meticulously crafted, better ones taking a year or so to make especially due to the hand polishing and ceremonial nature of crafting.
