Calling ron does not give you a yaku. What it will do is increase the fu count of your hand, but only if the hand is closed. However, winning from a ron on an open hand does not increase the point value at all; contrarily, you could instead claim a 2-fu bonus by winning on a tsumo.
Once your hand is opened, the only way to win is to have a yaku that does not rely on a closed hand. Opening your hand before you have a guaranteed yaku, or a good chance of building one, is often a mistake; not only does keeping your hand closed increase the number of yaku you can potentially make (especially "easy" yaku such as pinfu and tanyao), but you also have the option of adding the needed yaku just by calling riichi on an otherwise worthless hand.
If you do decide to open your hand, some common open-hand yaku which can be built follow:
- Yakuhai: A complete set (not pair) of dragons, seat wind, or table wind.
- Chanta: Every set contains either honor tiles, or at least one terminal (1 or 9) tile.
- Itsu: Three melds "123", "456", "789" of a single suit.
- Honitsu: All tiles, except for honor tiles, comprise a single suit.
- Toitoi: Every set is either three or four of a kind (i.e. no chi melds)
Some rulesets also allow a yaku for an open tanyao (no honors or terminal tiles). There are of course others, but I find these listed above are typically the easiest to make on an open hand, especially if you open early.
Even if you can't memorize all of the yaku-bearing hands yet, it's worth it to at least memorize these ones for when you choose to go the open-hand route.
That said, given the (incomplete) description of your hand, your best bet would've been to wait for a third dragon so as to claim a yakuhai yaku, and hoping to complete a pair involving one of your two bamboo tiles (while tossing the other). Calling chi on the bamboo actually harmed your hand, since you no longer had any reliable way to form any yaku.
Not knowing the makeup of your open melds, I don't know if calling chi on a
I Bamboo (instead of a
IV Bamboo) would've completed a chanta (or possibly an itsu) hand; even if it was possible, it would still be a risky wait as passing on the
IV Bamboo (while waiting on the
I Bamboo) would put you into furiten.