I tried selling one arrow at a time, but it looked like the progression bar was not moving at the slightest. Is my best bet to find a trainer?

I'm pretty sure Speech increases depending on how much value the item is worth (just like Oblivion). So say you sell an Iron Dagger it'd prolly increase it a small increment. Sell an Ebony Dagger and you'd get a substantial amount.

Once you get your Speech up to 40-50 range you can pretty much win any Persuade/Intimidate challenge. ONLY person I've had trouble with was Brynjolf of the TG. That dude truly has a tongue of steel...

Pretty much speech challenges and selling... OR find a Trainer to train you. I know some of the Khajiit's in the caravans can train you in Speech.

Go to Black-Briar Meadery in Riften and talk to the barkeep, Ungrien. One of his dialogue options has a Persuade check to have him tell the truth about Maven-Black Briar. That conversation option never goes away so you can repeat that over and over again to 100.

No wonder I thought I didn't see any increase in my progression bar... Is it weird that barter exp is based on volume, but other skill exps (one-handed, archery) isn't? I always thought it would make more sense if the exp you gained was based on the amount of damage done.
Yeah, I heard about that, but that seems like too much of an exploitation. I'm probably better off hiring someone to train in me speech.

Well Speech isn't exactly difficult to level up through other means. I don't like carrying more than 15k or so on me at once, so what I'd do is buy all the enchanted weapons/armor at a blacksmith then sell them back. Buying/selling raises Speech, so I leveled up fairly quickly there. Still, only a good idea if you've a lot of gold, but that's not really a difficult objective in Skyrim.

The master level trainer for speech is Geraud Gemaine of the Bard's College.

I'm not sure if you are saying this. But if you are saying that one-handed and archery experience gain does not depend on the damage done, just the number of hits, that's not true. It definitely depends on the amount of damage done. I did an experiment a while back, shooting the Greybeards with different bow/arrow combination.

There was a time when all I wanted to do is level stuff up for one reason or another but after playing Skyrim for every minute of every day since release I've learned to level naturally. Now I know your not looking for exploits from what I've read above so it seems you've already learned what took me over 500 hours to learn. The best way to level speech is by using making potions, enchanting and smithing. Those dot exactly give you speech but by using those to create items to sell you'll end up leveling them and and speech. Just collect anything and everything expensive and anything needed to create items, then stop by the enchanter, alchemist table and blacksmith's and create, then go to a store and sell those items along with the other items you have collected. You'll eventually level up all four skills. Try to find a good area that has lots of stores and a enchanter, alchemy lab and blacksmith. Best I've found is Solitude. You have a nice amount of people to sell to there. The fence from the thieves guild, a general store, a clothes/jewelry shop, an alchemist shop, a weapon dealer, an armor dealer, the wizard/Mage at the blue palace, your husband or wife at home if your set up for that and the group of merchants that have little amounts of money but still have money. I also found that putting your stuff in a barrel next to the blacksmiths works good, a nice central location, only put items needed to make things in there, stuff like herbs and leather etc. Be sure to switch barrels every month otherwise you'll lose it all.

I know my way seems a little elaborate but it worked for me and it just became routine.

Whatever you do don't go Riften and use that dude. It makes you feel cheap and cheated.

Actually, in Oblivion it was the opposite. It was entirely dependant upon the number of transactions, regardless of value. A Daedric Cuirass sold for 5k Gold would give the same amount of experience gain as an Iron Arrow sold for 1 gold. 10 Iron Arrows sold through 10 transactions of 1 would give more experience gain than 10 Iron Arrows sold in 1 transaction of 10. This practically forced me to download a rather useful "Toggle Quantity Prompt" mod for Oblivion, which allowed me to Control-Click something if i wanted to buy/sell/drop/pickup a single item out of a stack, or hold down Shift-Click to buy/sell/drop/pickup all items in a stack. Even with that though, raising Mercantile was ridiculously slow and tedious. Eventually a mod came out that made Mercantile gains based off of the value of the item bought/sold, instead of the number of transactions. Mercantile went up at a much more acceptable pace then, especially once i got to Lvl 20+ and was looting rather valuable equipment.

In Skyrim, i believe it is the value of the item that counts for Speech gains, not the number of transactions.

Ooh, I always thought it was the same as in Oblivion and Morrowind. I'm glad they changed it in this case then. And all this time, I haven't been using my best weapon or my amulet and ring that increases one-handed damages because it made my sword too lethal, and I feared that I wouldn't level up my one-handed in time.

This worked amazingly well for me. There really is no better way/person to do it than in Riften.

Actually in Morrowind it was the greater the amount that you increased the sell price or reduced the buy price that gave more to the Mercantile Skill. In fact, if you did not haggle, you got no increase in Mercantile. Speech was a different skill that had a tangent effect on Mercantile, but Mercantile had no effect on Speech. In Oblivion it was just .4 (out of 100) for each transaction, no matter how many items towards Mercantile. This is what we have in Skyrim, only I don't know how much each transaction gives to increasing the Speechcraft.

Note, on the PC, you can use the Home Key to quickly get to a count of 1 when selling multiple items.

Pickpocket a low value object and be sure to have the perk to bribe guards. Now bribe every guard in the town you did the extremely low bounty worthy crime in. Be sure you get caught, by the way, or they won't know you took a torch or key or low value bowel. Repeat this process in as many holds as you can or wait a few days in the same hold and repeat. I actually was able to get 100 in speech by doing this. The bounty has to be a bounty of 25, or it won't work.