What I would like to do...
Foldt,
I don't have a hammock (yet) but, when I have been touring before I would just leave the bike out. I have not had any problems before, but the foam seat on my recumbent has forced me to look for ways to keep this bike out of the rain. Plus, the components of the bike are better off out of the flying mud and such that we can get in our beautiful Kansas thunderstorms!
So, I am building a camping system based around the fact that I want to do 40-50 miles, camp at a predetermined location overnight, then turn around and ride home in the morning. This is why I want to use a hammock. I feel that it a very ultralightweight, comfortable, and most importantly compact system. Because the bike needs to be sheltered, and I am going to be exposed with nowhere to hide, I am leaning toward a larger hex tarp.
Also, I am very concerned with weight. I will be arriving at camp with just a few hours until bed, so I am not planning on bringing a guitar and axe so I can build a fire and sing Kumbiya... :D Basically just a hammock, tarp, bugnet, clothing based on the weather, and bike tools. I know this may sound boring, but I find after 50 miles of riding, I don't want to go do much! ;)
A few things about handlebars as spreaders...
1. When you are talking about using the handlebars, are you imagining straight mountain bars? A majority of tourers are using curved handlebars much like you would find on a "road" bike. The advantage with these bars is multiple hand positions, which are very important on a tour where you are on those hands for 7 hours+ a day. Now, you can add what they call "end grips" on the end of your flat handlebars, but to use them as a spreader, you would have to remove these, as well...
2. Although, that doesn't mean you couldn't use a mountain bike for touring, but the frames are built heavier on mountain bikes, so you are already paying a weight penalty that could be on the order of 4-10 lbs depending on how much you will spend on the bike.
Now, you could look into what they call "hybrid" bikes. These bikes have road components, frames, wheels, but they have flat handlebars and mountain bike brakes and shifters. Nice compromise...And trust me, the skinny, high pressure tires and shedding that amount of weight (compared to mountain bike with heavy frame and large inefficiant tires) is huge!
3. I wouldn't want to remove my handlebar every time I got to camp. But sometimes ultralighters do things like this to accomplish a versitile, lightweight setup...more power to ya!
After thinking about it, I would agree that using the bike itself as a support for the hammock is not something I would do, either! I think it could be a support for a tarp just fine, though. Perhaps someday I will try it, but I would rather not! :D