There are a lot of options! I've used blue tarps from wally world, sportsmans guide 12' tarps, and I've tried a DIY tarp (it was too heavy using 1.9 coated nylon so it became a spray cover for my Bell canoe)
The most bang for my buck so far has been the HH Hex tarp in 70D nylon. I found one on Amazon for $70. It covers well and is under $100.
It is in no way equivilant to the cottage venders here and it don't have doors but the coverage good enough and at 1 1/2 lbs not too heavy
I haven't needed doors yet, I am going to try my frog toggs poncho as a door this spring to see how well it helps. Usually I can get by with site selection by pitching the hammock so one of the sides of my tarp will go to the ground and block the wind.
I think you could get all of your gear and a bike under it if you pitch it in "porch mode". I usually hang my extra gear in a smaller hammock chair/gear hammock under my sleeping hammock. Does your bike have its own stand? (mine don't) if so, you could possibly hang gear on it under the tarp. My tarp don't usually cover all the way to the tree if you were planing on resting the bike against the tree.
Hope this helps