Hi:
I just installed a GE water heater and noticed that there are drips of water where I connected the adapters to the nipples. I used Shark Bite 3/4 inch adapter, also used teflon tape.

Is it the taped joint or the shark bite joint that's leaking?

It seems that the Shark bite fittings have very specific assembly instructions. http://www.cashacme.com/SharkBiteInst.pdf

It is the taped joint

Here's instructions:

Plumbing Repair Guide: How To Use Teflon Tape - ACME HOW TO.com (http://www.acmehowto.com/howto/homemaintenance/plumbing/general/teflon.php)

There are a couple of things that can go wrong. Going all the way to the end sometimes pulls and tears the tape.

Here is a discussion about tighening NPT threads.

How tight should you install a NPT fitting? (http://www.mechanicsupport.com/articleFittingTight.html)

NPT is National Pipe Thread and it's a tapered thread, so it will either seal or rip the teflon tape. As the link above states, you need to get a feel for it.

How clean were the threads in the tank? They often come from the factory with crud in them. You may need to remove them, clean up with a wire brush, and reassemble.

They we clean, but this begs another question. The nipples had a blue plastic insert for cold water and a red insert for the hot water... should I have removed them before I attached the adapter?

Those are dielectric nipples. If they had little flaps sealing them, I would remove the flaps. Either leave the inserts in, or pitch the nipples. Flip a coin after reading https://www.askmehelpdesk.com/plumbing/dielectric-not-dielectric-151348.html