I started and to use a bow and arrows right when I got one. They freaking rock ... however im running out of arrows and im in the middle of nowhere (Heading from the jail to the person I have to give the dragon pendant to [first mission]). I have 16 left and sometimes I can't remove them from my enemy's head.

Every town (including the one you're going to) has a weapon shop that should probably have some arrows. Other than that, you'll just have to kill enemies for them.

Get a pair of pliers! (I'm kidding!)

If I were you, I'd hit the Imperial City Market District before heading anywhere. Sell all the junk you can at a place called Rindir's Staffs. The guy running that place has low merchant skill. Remember to haggle! You can pick arrows up at... that store next to the Merchant's Inn (drawing a blank on the name).

Slash and Smash might have arrows too.

Also fighting bandits are a good way to get arrows.

Why pay for something you can get for free? Just go to any fighter's guild when someone's practicing marksman and steal their arrows before they pick them up. They apparently don't mind.

Try the Archer's Paradox in Bravil.

Most smith shops probably car some assortment of arrows. Also try Thorinir over at the Copious Coinpurse in IC Market District

I don't recall ever buying an arrow, and I've played a lot of archer characters. Bandits are the usual source. Starting from the Prison sewer, there's a bandit archer right across the water at Vilverin. There are several others down inside that ruin.

There are almost always bandit archers at the roadside camps, too.

Also, get a better bow, which does more damage, and your arrows will go further. There's a Fine Steel Bow available with only moderate jumping required at: