Sword terminology is. . . messy. But the true reason for the term 'bastard' sword is exactly what a few others have mentioned. It is a hybrid sword - capable of being used two-handed with ease, but just as capable of being used with one hand. It is, thus, neither truly two-handed, nor truly single-handed. It is a combination of the two - a bastard sword. The term is fairly old, but actually didn't, apparently, come into use until two-handers did. And the 'bastard' sword predates true two-hand swords by quite awhile.
Just as a sidenote on two other terms:
Broadsword: Totally useless term. The term came into use to describe -any- sword wider in the blade than civilian swords of the time (rapiers, and later - smallswords). Therefore, the term refers to practically every military sword used prior to, and well into, the 17th century. Therefore, the term should never be used to describe any particular sword, because it's neither precise, nor truly accurate.
Longsword: Longsword (or long-sword) has seen a lot of use historically. In -modern- vernacular, it refers to a 'bastard sword.' Longsword now meaning a sword that is long - yet is not a two-hand sword (and even then, some modern enthusiasts will use the term to describe a sword which is clearly a two-hand weapon). But historically, the term's meaning changed over time. There is some indication (though I can't remember from where now) that the term 'longsword' was originally used to describe single-hand knightly swords, as they were .. well. .long. For their time, at least. When longer swords came into use ('bastard swords') the term transferred to those, as single-hand swords were no longer 'long,' as it were.
Either way, D&D has made sure that the term 'longsword' is totally identifiable to non-sword enthusiasts as meaning a single-hand knightly sword. That can cause some confusion between those not learned in the subject, and those learned, as the learned refer to 'longswords' in the modern (and 'correct') usage of the term.
As I opened with - sword terminology is messy.