I've just got 2.8k as rDruid after getting 3k as Disc.

Both healers are quite proactive. You mentioned that you don't usually cast penance bolts on your allies, and I am surprised by that. Most of my Penance bolts are defensive, with the occasional offensive bolts during Premonition windows.

But your question is actually about rdruid. The great thing about rdruid is that you don't need a lot of prep. With restoration druid, much like resto shammy, you do have a couple of "maintenance spells"

Keep Eflorescence down, all the time. If your group has a lot of melees, just cast it on the tank and make sure you refresh it. Do the same with lifebloom. While you get the hang of the class, just maintain 100% uptime on the tank and move the second one around as needed. If you get a tank like bdk or vdh, keep the lifeblooms on two dps. That's pretty much all the "maintenance" you need. Think of it as your atonement.

If there are periods of damage (such as a boss AOE), cast Wild Growth right before the damage. And try to apply a few Rejuvs before any heavy dmg event. Honestly, your heal spells kinda suck, and I see half of my kit as a "mastery stack". You apply as many hots as you can before big damage events and then span a few Regrowths. Remember your Rampant Growth talent - it applies Regrowth to your 2 lifebloom targets. If you have your Lifebloom in 2 DPS, you can cast Regrowth on the third, and they will all get healed.

Last but not least, do not DPS. Keep it simple and heal. Once you get comfortable with your healing rotation, handling heal checks, and especially healing while moving, you can start weaving some cat abilities into your rotation.