Just eliminate it entirely as a really poor design decision in the first place. It’s totally not necessary.
The effects of the template should be role-played. So the character should have to struggle with primal urges and the like, and the player should try to make this interesting and part of his character’s story. But his alignment should not arbitrarily just change. The alignment change should be treated as a thing that happens to the weak-willed, perhaps, or to commoners unprepared for the magical assault on their bodies, minds, and souls (as adventurers, even low-level ones, might be). It might be a thing that could happen to a player, if he indulged those urges. But not automatic.
I don’t particularly like the idea of Will saves vs. compulsion to enact said urges. A good roleplayer shouldn’t need to be forced, and ultimately the effects of a few bad rolls in a row could be very problematic for keeping the player’s character as the character he wants to play. This kind of mechanic could be done well, but ultimately I’d rather just make it a plot-device that the player can play with. And if the player isn’t interested in doing so, then I really don’t think making him roll Will saves is a good idea: it is a game, after all. Forcing the player to “play” a game he doesn’t enjoy doesn’t make much sense, and strikes me as rude.
“Always” alignment does not actually mean always
Always: The creature is born with the indicated alignment. The creature may have a hereditary predisposition to the alignment or come from a plane that predetermines it. It is possible for individuals to change alignment, but such individuals are either unique or rare exceptions.
Note that creatures with acquired templates do not experience “birth,” so the first line does not apply. Becoming a vampire “always” changes one’s alignment, but in rare cases (perhaps as in the case of your NPC), that can be subverted.
And even in the cases of Evil vampires, they can be reformed. There’s even an explicit spell for doing that (santify the wicked from Book of Exalted Deeds), though I strongly encourage you to completely ignore it as it’s very poorly designed (like most of that book), and has some extremely unfortunate implications (if you ignore the fact that the books says it’s good, and read it, it sounds like a pretty awful, evil thing to do to a person).
Thus, yes, you can have a non-Evil vampire. Redeeming Evil creatures is not just a Good act, it is the quintessential Good act.
That said, no character is ever required to always act for the maximum Good; it is not an Evil act to choose to not perform a possible Good action.
That said, assault and murder are pretty much definitively Evil...
Evil Alignment is consistently not an acceptable reason to attack someone
Attacking someone without specific cause is assault, which is Evil and in most jurisdictions illegal. Continuing that assault until the target dies is murder, which is definitely Evil and illegal most everywhere.
A paladin who attacks someone purely on the basis of pinging for detect evil should, under the rules, fall on the spot, for willingly commiting an Evil act.1
This is described in multiple rulebooks. It’s one of the few things about alignment that actually is somewhat consistent.
Alignment is not a detailed or consistent system
Alignment is described in different ways in different books, and the definitions are vague, ambiguous, and conflicting. The system is a historical artifact of D&D’s roots: it is designed for a simplistic, hack-and-slash dungeon crawl, where the players are Good because they are the players, the goblins, orcs, and vampires are Evil because they’re the enemies, and no one ever thinks too hard about that. Unfortunately, D&D has evolved but alignment hasn’t evolved with it; though people play far more serious and varied games than a straight dungeon crawl, alignment is still the same nine boxes. Don’t expect much from it; I actually strongly encourage you to ignore it. Outside of those simple dungeon crawls, it causes more headaches and arguments than it will ever be worth.
1 I cannot more strongly recommend against the actual falling rules, however. Instead of stripping the paladin of class features (boring, interrupts the story, punishes the player), I strongly recommend switching the character to the appropriate alternate alignment variant paladin, so he keeps his powers they just become “dark” (or chaotic if that’s the way he falls).
Best Answer
It was an act of good by D&D standards
D&D has a very black and white approach to morality. Killing an evil creature is an act of good because there is one less evil creature in the world. Had the bugbear surrendered and then been killed, it would then be a case of lawful vs chaotic as well (and is a good starting place to get the players to think about the other axis of their alignment)
It does of course depends on how tightly you play by the alignment rules. If you were running a game in which morals played a large part, it could of course be considered an evil act. After all, are you any better than the thug you just killed? What about the family he was trying to feed? But if you are playing that sort of game, the players need to be told up front that you are deviating from the norm.
Though there is another point work making: One action does not an alignment shift cause. Performing an act of evil is just that, a single action. While there are actions that are large enough to justify an alignment shift, generally speaking it is the sum of the characters actions that determine their alignment overall.