Need Recommendations for Flat-Bottomed Hammock

First, welcome to the forums. Second, though I am no hammock expert, I believe your hammock is probably the Bear Mountain Bridge Hammock. You might consider checking in at hammockforums, you will find a dizzying amount of information there.

Do you side sleep? If not, trinity is right, you probably want to look into a bridge hammock. Separate nets can be purchased that enclose the entire hammock, so don't think you must limit yourself to a hammock with an integrated bug net.

If you side sleep, the Grand Trunk Skeeter Beeter Pro, at 11ft, has an integrated net and can be set to sag nicely and allow for you to lay diagonally in it. The hammock is particularly wide and I tend to side sleep more. This has been a very comfortable hammock for me. The hammock with net, cordage, and tree straps weigh in at about 2.5 pounds (1.1 kg) but it can me made lighter by changing the straps it comes with, swapping out the beener on either end, etc. They normally run only $80, but can be found cheaper if you look for sales, sometimes as low as $50. If you add a nice tarp to this, you can have a solid shelter.

Drop by Hammockforums and take at look at the gear they have for sale, you will see a number of options. Go to youtube and search bridge hammocks and see the number of reviews that come up for a variety of them. Also, check out Sean Emery, he goes by the name Shug, lots of great vids and gear review from him.