Unfortunately, bullets, knives, and arrows are a bit like apples, oranges, and lemons when it comes to comparing them in this way.
The majority of bullet-proof vests are lousy against knives. In fact you will find that bullet-proof vests are one kind of body armor, whereas stab-proof vests are another.
Kevlar and nylon are commonly used in bulletproof vests. Without getting too technical - these are fabrics. Tight-woven, metallic fabrics yes, but still they operate on the principle that they can take a bullet and slow down its impact over time and area. A knife - which comes in slower than a bullet, much much slower in fact - can move between the threads of the fabric and meet the target. Stab-proof vests are different entirely; they're thicker and sometimes have protective plating, and they owe their design more to chain or plate mail than bullet resistant vests. On a smaller scale, the practice of using mail gloves as hand protection in professional kitchens and/or butcher shops - an environment where you find an awful lot of knives, in other words - is still practiced.
So really, these are all very different kinds of impact that are best deflected in different ways. It isn't a linear progression from arrow to knife to bullet; just because times have changed and firearms are theoretically more advanced than bows and arrows, does not mean that they are more effective in every given situation. To put it another way - it isn't an RPG, moving from bows to bullets is not strictly "leveling up".
It is entirely sound, therefore, that Data can and has sustained penetration damage from held weapons and arrows, but bullets are significantly less threatening to him.
EDIT: Assuming none of the players involved are fabricating any materials or saying something is what it is not, observe this 50lb longbow penetrating modern bullet resistant technology:
So consider Data's structure. According to Memory Alpha, Data is made of the following:
- bioplast (his skin)
- tri-polymers (polymers used in - dun dun dun - fabrics commonly)
- polyalloys (his supports or 'bones').
To hazard a guess - the polymers act as (or simply mock) musculature. The skin is probably useless as a protective layer, and it's shown to be porous under magnification and can be scraped off by glancing blows from a pickaxe. The polyalloy frame would absorb raw impact (per The Chase) however his actual skull is made of duranium (starships are made of duranium). His body, probably being mostly that tight-woven fabric-like tripolymer, would then be fairly catagorized as a substance that is built to resist bullets, but predictably buckles under piercing weaponry.