Yeppers, that's how it is done. If you hold the bow with your left hand, the arrow groove in the grip is indented on the left side, so you have to knock the arrow on the left. Of course, there are grips where the groove is to the right, if you hold the bow with the right hand. Choosing a bow with leftedness or rightedness depends on which of your two eyes is your "dominant" eye.
I feel Bethesda could really open up archery by adding on accessories and having well-crafted bows. All of Beth's bows - in Oblivion, in Morrowind - look like crap. The screenshot of the khajiit with the bow - that bow also looks like a piece of crap. No one makes bows like that, not even back in premodern times. I can see compound bows being a Dwemer technology, since the pully system requires precision to manufacture/craft the wheels. Other than that - I'd like to see some recurve and compound bows, please!\
Any of you use Nicoroshi's bow mods for TESIV? Those are what kickass fantasy bows should look like. And Phijama's TESIII bows are great, too (recurve, etc. modern design). http://planetelderscrolls.gamespy.com/fms/Image.php?id=26867. http://planetelderscrolls.gamespy.com/fms/Image.php?id=26871 in game - notice how the groove is to the right, since the bow is held in the right hand.
EDIT: Right, I mentioned accessories. Silencers and aiming devices spring to mind.
The groove determine the hand of the archer, right. Left sided groove, left handed, right side groove, right handed.
But in earlyer times there was no grooves, grooves came with conposite materials.
Bow wheren t uniform, most of the time the shooter side was more linear than the opposite side, (although i ve positively seen exactly simetric simple wood bows) and the groove was actually your knuckle. Thats why archer used to use gloves on the bow hand, because the feathers passing over your skin does a clear cut. And when you have to shoot dozens of arrows, your hand would not be something nice to take a look at.