The technology behind the spear is pretty simple: pretty much, you find a pointy stick, and you're done. Over time people learned that if they rubbed something on a rough rock, they could make it sharper. Then they cut out the middle man and just shoved the rock on the end of the stick. You can affix it with friction in a pinch, but some bit of grass or sinew works better. But remember these are just improvements. It's still basically a pointy stick.
Versus the bow
Comparatively, the bow is a magical instrument. Think about it from the perspective of your average prehistoric spear-throwing thinking person: the idea that you can take a (smaller) pointy stick, and instead of throwing it, you pull back on a tiny little string (what's that?), let go, and the stick goes forward, far faster than you could ever throw it, and that a smaller stick with less work from the wielder could be more effective than a big stick? All of that would likely seem extremely counter-intuitive and come as a huge surprise, possibly with rather violent disagreement.
Thus, while I admit I don't know what actual steps we took between the spear and the bow, I bet history will back me up on at least this basic theory: several other key technologies would have to be invented between that first pointy stick and the bow. Those would probably include rope/twine/sinew, basic knots, (leading first to better spears), then slings, snares, springy things leading to mechanical advantage, better tools, crafting methods, and so on.
Had we developed those technologies c. 100,000 years earlier (based on your dates), the humans of that era wouldn't simply be better hunters and warriors.
Smarter, faster, stronger
They would have better tools, they would be smarter hunters, battle tactics would evolve. Defenses to long-range attack would come sooner.
What about our old friend, the pointy stick?
I think that despite the early adoption of the bow, the spear would still be just as useful throughout history (after all, it's still useful today!). The bow is not universally superior: even modern military rifles are still sometimes fixed with bayonets.
Women might participate more heavily in combat, as drawing a bow requires less upper-body strength than throwing a spear or swinging a bludgeon. Whether that would help equalize gender roles or not might be an interesting question to explore.
Global spread (and beyond...)
Once we spread across the globe, every civilization would have a much higher starting level of technology than we did historically. Very often these types of "small" changes (and I don't think this is a small change!) have compound interest (i.e., exponential growth) effects over longer timescales, meaning that by 2016 in your world, who knows, we might have developed the technology to spread halfway across the galaxy by now!