So your sword wielder has superhuman reflexes, but he'll also need some degree of superhuman strength to hold a bulletproof sword while it deflects a bullet. With that being said, there are a number of materials capable of withstanding bullets:
ALON Transparent Aluminum
Known commercially as ALON, transparent aluminum armor is made of aluminum oxynitride, a combination of aluminum, oxygen and nitrogen. Before it can end up as a hard transparent armor plate, it begins as a powder. This powder is then molded, subjected to high heat and baked, just as any other ceramic is baked. Once baked, the powder liquefies and then quickly cools into a solid, which leaves the molecules loosely arranged, as if still in liquid form. The resulting rigid crystalline structure of the molecules provides a level of strength and scratch resistance that's comparable to rugged sapphire. Additional polishing strengthens the aluminum alloy and also makes it extremely clear.
Now, just as bullet-resistant glass is made of three layers (two panes of glass and a middle pane of polycarbonate), so too is transparent aluminum armor. The three layers, consist of the following:
Not only can the aluminum armor deflect rounds from small-caliber weapons and still be more clearly transparent than bullet-resistant glass that's been shot, it also passes a much more important test -- a 1.6" thick pane resists .50-caliber armor-piercing bullets and anti-aircraft weapons that typically use .30-caliber rounds. This is an impressive feat, especially since it's half the weight and thickness of traditional transparent armor.
So, a 1.6" thick sword is thick, but relatively lightweight, and can stop a direct hit from armor piercing rounds. A thinner version could probably easily stop .22 rounds. So that's one possibility.
Composite Metal Foam
Composite metal foam (CMF) is made by bubbling gas through molten metal to form a frothy mixture which then sets as a lightweight matrix. This leaves a material that offers a lighter alternative to conventional metals, while still maintaining a comparable strength.
CMFs have been used to create high-strength armor comprised of boron carbide ceramics as the strike face, with CMF as the bullet kinetic energy absorber layer and Kevlar panels as backplates. To test its durability, such armor was tested against a 7.62 x 63 mm M2 armor-piercing projectile, which was fired in line with the standard testing procedures established by the National Institute of Justice (NIJ). This armor could stop the bullet at a total thickness of less than an inch, while the indentation on the back was less than 8 mm. In fact, not only did the armor stop the bullet, it turned it into dust. To put that in context, the NIJ standard allows up to 44 mm (1.73 in) indentation in the back of an armor.
So, this type of material could be incorportated into a sword to make sure it was strong enough to deflect or stop bullets. You might need to have a significantly wide sword, depending on how thick the materials are, but a wider sword could still be useable.