Thanks for all the advice guys. I have since pulled two more from that mould, and both turned out great. I think allowing it to FULLY de-gas has helped tremendously, and heating the resin and mould makes a world of difference too.
For these parts, I am using 31grams of mixed epoxy, and it takes about 5 minutes to fully de-gas. I am using infusion grade epoxy, and have degassed at full vacuum and it doesn't appear to boil off any solvents (as it still hardens at the end of the cure cycle). I definitely see this as a problem with other epoxies, so it is a good thing to be aware of, but it doesn't appear to affect the epoxy I am using.
The nice thing about my setup, is I can de-gas the epoxy right in the resin pot, and then remove the vacuum line and begin infusing right away. It eliminates the air that would normally be between the epoxy and the line clamp to begin the infusion. The picture below is the modified cup

The plastic cup I am using is actually from the local dollar store, and has a silicone seal for its lid. I just drill and tap a couple connectors on the top and bottom, and now it is really easy to see how fast the resin is being sucked into the part. This works nicely for testing new moulds where the exact amount of resin required is unknown. The cup is also double walled, so if I ever get fancy, I might include a water-jacket in between the two walls to help regulate heat inside the resin pot.
Anyway, here are two pictures of the new, untrimmed "teardrops" with no bubbles or imperfections.

Teardrop #2

Teardrop #3

Teardrop Mould
As a side note, I have found it very easy to place the fabric inside the mould even without using any spray-tac. I used the first teardrop mould as a buck (the one with bubbles and general nastiness) to press the fabric into place inside the mould. While I hold it there, I tape down the edges of the fabric to the flanged area on the mould. Now, when I pull the teardrop shape buck out, the fabric is well placed. Then, when I am setting the vacuum bag up, I begin by placing the vacuum bag around the teardrop shape buck and set it into the mould. This way, I know the vacuum bag will be able to reach the inside and not create any bridging. It has worked fantastically well, and while it may not work on every mould (especially ones with a really thick layup), it certainly worked here.
To summarize, here are the important steps I have learned from these tests.
1. Always fully de-gas the resin. It makes a huge difference in the amount of bubbles that travel through your part. Visually, once the resin reaches the vacuum port at the end of the part, there were noticeably less bubbles as compared to when I did not de-gas.
2. Heating the mould and heating the epoxy makes everything easier. It allows the epoxy to flow much easier, it de-gases faster, its just a plain old good idea when infusing to warm everything up. I want to get an infrared thermometer to measure how just how warm, "warm" should be.
3. Ensuring that there are no leaks is insanely crucial. I saw on another forum that some people will infuse as long the leakdown test does not drop more than 0.5inHg in an hour. I have had infusions that came out perfect with 0.5inHg leakage per hour, and have had infusions that have failed horribly with 0.5inHg leakage per hour. So I don't know where I stand yet on this, but I am certain through my tests above, that a leak is what caused the resin to climb back up the resin feed line on my original panel. I think NikCFC is right about the bubbles, so find those leaks! Regardless, check out Fred's post about sealing edges of infusion mesh and spiral tubing.
4. Think of how gravity/buoyancy will effect any air inside the mould. This is still in the testing phase, and I am certain it is not necessary if you have a fully sealed bag, but on both successful infusions of the teardrop, I setup the mould so that the resin inlet was below the vacuum inlet. I did this because I noticed something very interesting about the first failed infusion of the teardrop. There were bubbles trapped in the part, but they clung to the carbon fiber, almost as if they were trying to rise to the top of the part (on the backside), but were blocked by the fabric. I figured I could avoid this in my next teardrops by letting gravity/buoyancy allow the bubble to rise up to the vacuum inlet, in hopes that they would get sucked up. Again, I doubt this has any relevance, especially if you have no leaks and have de-gassed properly, but it is something I will try to test and determine its effectiveness.
Overall I am pretty happy with my procedure now. And I do want to thank everyone who has pitched in some information. I hope to keep posting and updating with new tests and projects on this thread. Now what to do with all these random teardrops? Christmas ornaments? I should have designed a testing mould for something that was useful haha.
But onto my next question. I saw someone mention that you HAVE to have your vacuum pump operating at a higher location than your resin pot for a good infusion. I could not for the life of me think why that would be the case. I can't ask him as his post is a couple years old, and I don't think hes been active on that forum for a while. So fellow composites people, any ideas why?