You're right that it's hard to have decent mana regen without Meditation, especially for long battles. However, I find that if you're running out of mana on anything shorter than a five minute battle, either you're not using the most efficient spells for the task at hand, you're overhealing, or you're not stacking enough spirit. Something I learned the hard way: All the +heals (or +spellpower, now) in the world won't help you if 15 casts is all it takes for you to go OOM. Give up some of those +12 Spellpower gems and put Spirit gems there instead.

Are you remembering to set your shadowfiend out *before* you're out of mana? If you balance things just right, you can find a nice chain for especially long fights: I use my fiend when I'm around 40%, which usually gets me in the 90-100% area, pop a mana pot around 60%, again at around 30%, and can usually use my fiend again before I'm OOM, bringing me back up to around 60-75%. Of course, depending on how heal intensive the battle is, you can take turns with the other healers in taking a break in casting to allow regen, before you're tapped dry. Bangle of Endless Blessings or Earring of Soulful Meditation are both very helpful with this tactic.

I can't compare druid regen to my own, but I find that if even with all this, if you're still pushing it to the limit, and running dry before the battle is over, make friends with the Druids you run with (especially feral!) and stack spirit. In a tight spot, give them notice that you may need an innervate, and when they find a moment, they can send one your way; with enough spirit, you don't even need to stop casting to go from bone dry to 100% mana. If you're low on spirit, one of the trinkets above can be popped just before you are Innervated to boost its effectiveness.

I hear you on the mana shortness... things don't get much easier in Shadow.

I have found a few things that help though...

As the person above said, definitely stack spirit. Before 3.0.3 I was all +damage, now I'm all hit, crit, some haste and spirit, spirit, spirit. There was actually a lot of synergy introduced into the Shadow spec. Twisted Faith in the Shadow tree takes the edge off of chucking all those +dmg gems for spirit (or dmg/spirit). Imp Tap will increase your Spirit on certain crits and will give you extra in-combat regen... and extra Spirit means extra damage with Twisted Faith.

Stack crit. Crit is one of our go-to stats next to hit and spirit. In Shadowform your crit chance increases the damage of your dots. Let me say that again... your dots' damage is increased by you crit chance. So... if you have 10% crit, and sw:p, VT and DP up on a mob, then pop Shadowform, the damage done by each dot goes up by 10%. VT's spell coefficient was reworked as well so that it does much more damage. I've seen it tick for over 800 once I stack up some Shadow Weaving. Plus.. everything we have can crit.. including dots. So, be sure to use your dots effectively and stack that crit.

Now that downranking was removed you can't actively control your mana at the level we used to. You can't say 'well, I want sw:p, but full rank sw:p is too expensive, so I'll cast a lower rank'. Now you have to choose between using the spell... and not using it. In general you have to be more selective about what you cast when. In effect, every spell we have is now kind of 'situational', since we just can't afford the mana to stack them all.

That said, VT takes as much time to cast as MB, does pretty close damage (with a lot of crit, it could do more) and costs quite a bit less mana. When I'm soloing, I cast shield, VT+flay+flay ... that's pretty much enough for anything I run up against. If you're trying to stack up a pack of mobs, the key is to proc Imp Tap and Spirit Tap as soon as possible for the damage boost and regen. VT+DP the 1st mob, VT the next, VT the next, fear, MB or flay the 1st... you should kill it, proccing Spirit Tap... then... have fun. In general I don't pull sw:p out of the box unless absolutely necessary. It costs waaaay too much mana to use regularly. It goes on bosses and elites only. If you're dealing with a group pull and need some AoE (I havent gotten mind sear yet, so I can't talk about it really), VT+tab 3 mobs, then flay around.. use mb on mobs around 4 to 5k (or sw:d around 2k) to try to catch the killing blow for that sweet, sweet Spirit Tap proc.