Eridium drops everywhere but there are no reliable farming methods in the early game. The slots mentioned above are down to RNG, and areabout as reliable as killing random enemies.
Additionally the cost increases with every purchase (4, 8, 12, 16, 20, 50, 100, 150, 200), so you’d just be wasting time. It’d be better to just progress your missions, and you’ll get Eridium and then turn it in whenever you are in Sanctuary.
I think the more important thing to examine is the fact that you are running out of ammo frequently. My suggestion would be to consider checking your weapons and making sure you are constantly upgrading your gear, the most common cause of running out of ammo is because you are using low level gear. Having a backup that is of a different weapon type, also helps.
Although I do suggest popping open all the lockers in the Crimson Raider headquarters every time you load the game. And maybe check the ones in Scooter’s garage too if you really need just a bit more.
That. Sanctuary seems to have quite a few scattered around: I tend to farm those two areas first, plus what’s in Docs. I even found the two boxes outside Moxi’s (right of the south entrance) contained one lump in each, so it’s in the most unlikely places.
Check every moneybox, crate and locker you encounter in maps – one that regularly has a coupla bucks in one day suddenly has a glistening purple bar. Also break every crud pile you can find: icebergs in arctic places, spiderant dung in Frostburn, steaming heaps in Three Horns… they’ll contain ammo and occasionally will give up a weapon or Eridium lump. I’ve picked up purple and blue items from these alone around Southern and 3Horns.
I maxed out my backpack first (so I could carry more and build cash faster), then looked at upping the ammo capacity. I think I’ve only upped grenades and sniper in the first instance, but tend towards elemental weapons for greater damage.
As others have said: you’ll find more Eridium drops the later you progress, so you’ll find it fairly scarce in the earlier maps but pretty commonplace once you get to the mid-later stages. I’m at the stage of grabbing 20+ bucks from cash boxes that I’m ignoring those in earlier maps.