After extensive research on the wiki regarding statistics and a little (not enough) testing I'm confident enough to tell you about my first build - jungle. Jungle Zyra is squishy but, because of her plants, she has a very fast clear time. She may start off slow (literally) later turning into a mage plants assassin roaming the map. Because of her utility skill-set her ganks are very powerful and few typical junglers can match her ganking power (though speed is not her strong suit)
Give Zyra a hard leash on blue as her early jungling is exceptionally weak without her plants. The CDR is very important to your jungle clear time. Your plants tank damage before you sparing you actually quite a bit of damage therefore increasing the amount of time you can spend farming the jungle. Enemies deal fixed amounts of damage to your plants because your plants have only 6 health. Champions deal 2 damage to your plants while jungle monsters deal 1, allowing each plant to tank 6 auto attacks before you take damage (exceptions beingand dealing 4 damage) from both and , effectively making you avoid 12 auto attacks.
My masteries are 11/9//10 taking AP per level, 2% bonus dmg in Offense, enhanced smite, armor and flat health and per level in Defense, and mana regen, move speed, summoner spell CDR and buff duration in Utility. My runes are physical dmg red, armor yellows, flat AP blues, and flat AP quintessences. These runes should increase her early on hit damage and spell damage just giving her all around damage but the give armor too which she needs to survive for longer as she has no natural sustain. You can opt for spell penetration vs champs but seeing as it only ignores MR as opposed to lowering it, it does not enhance damage to monsters because they already have 0 MR.
My starting items are machete 5 potions, for early damage. You want to grab Zyra's Q first for the AoE but afterwards grab seeds and max your Q by level 9 because your E is purely for utility so max it second (the blue buff will keep you from needing the CDR of your plants) Using the blue buff leashed to you, you can clear faster because of increased seed generation. You may choose to build eitherfor the AP and survivability because it is an incredibly gold efficient item and you may not have enough money (if you didn't get any kills or assists) to afford or for the sustain. Plants also benefit from spell vamp as if they were single target spells giving you some good jungle sustain especially if you choose to build before Armguard. Plants deal only magic damage and do not proc red buff.
Keep in mind that Zyra's plant are considered traps likeand not pets, so you should stay away from despite it's survivability and similar damage boost and AP. Use your 5 potions and plants tanks correctly and you can stay in jungle a long time. The damage boost from will further increase your clear time as well as increasing the damage your plants deal to monsters (just another reason to avoid Banner of Command)
Also, to increase your clear time even further, you need to buildor else your ganks may fall flat in both deliverance and damage. Take it from here folks. From this point on in the game she can be build like a normal mage tough I do recommend finishing as well as taking a for the utility. Positive feedback, please :)