The statement above that people didn't use them and shields at the same time is false - they were most commonly used with the other hand consumed with something else.
When used two handed, they were hefted (in D&D terms, slashing).
When used one handed, they were used more like an Epee (rapier).
They were also one of the first swords that featured a blade guard that curved down behind the fingers - but not to protect the fingers. It was actually used to grip the sword half-sideways in order to be able to quickly slash something one handed without breaking your wrist.
Many different tactics were used with the blade and if you wielded a shield, you cut yourself from that versatility, forced yourself to use only one handed techniques and the sword wasn't optimized for it. It was too long to be a good one handed slashing weapon and a thrusting style couldn't use a shield larger than a buckler without it being a serious hinderance. Fighting one handed could done, but it couldn't be done better than with a dedicated one handed weapon.
Beside powerful two handed slash, half-swording techniques (gripping the sword halfway on the blade to wield it like a shortt spear) were extremely common in order to punch through hard armor. With a shield, you can't do that.
One handed, it was best used to thrust. But it was hardly an excellent one handed thrusting weapon. The sword was versatile, but only as long as both hands were free. If you had a shield strapped to the left arm, versatilty was gone and you were left with a sword inferior to a pure one handed weapon.
But that is mostly moot; by the time the bastard sword was rising, the shield was dying.
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There is bound to be a lot of opinions in any comments about how to use swords from the longsword family (such as the bastard sword). Not a whole lot of hard documentation exist.
So I guess a IMO should be attached to the post with the mention of minimal personal experience (I've done some fencing, martial arts and had in my hands a few a middle-age weapon replicas).
The Flower of battle is one of the only books with solid info on what the sword master of the era taught and pretty much the basis of any expert opinion of middle age martial arts. Never read it, but read books quoting it (amusingly, first time I saw it used as a source and it came to my attention is by the Riddle of Steel RPG!) and it seems to me that the consensus was that swords longer than the knightly arming sword use in the 12th century should be wielded either two handed. There is a section talking about the benefits of occasionnaly doing one handed maneuvers but it's not the meat of the book. Personal experience, for what little it is worth, also tells me that. Then, later masters would developp one handed fencing with its focus on thrust; swords would be refined for this purpose along with these development and in fact the bastard sword maybe seen as one of the early step toward that style. But it's not nearly there; fighting a purely thrusting style with bastard sword seems unwise to me.
Personnally, in real life, if catapulted through time and forced to choose, I'd never consider wielding a bastard sword without having my other hand free (maybe with a buckler; I have no experience of it and no real idea of what it'd feel like). If I had to wear a shield, there are dozens of other weapons I'd prefer using, from the roman gladius to a simple, appropriately sized club!
