The basic premis being security and protection from the weather, however one added advantage is being able to use the bike as a structural element instead of carrying poles.

Thus far I've only seen a couple bike specific tents, neither of which really capitalized on the structural advantage a bike has to offer.

However, I just stumbled upon the following excellent example of how to use a bike to support a rainfly.

http://www.crazyguyonabike.com/doc/page/?o=3Tzut&page_id=104126&v=H#pic_467817

Just looking at the pics is worth more then I can illustrate in writing, but let me try to sum up a few of the points I found interesting.

1) Basically the guy uses the highest point on the bike, the seat, to support the apex of his rainfly. Thus the rainfly is theoretically high enough... though being 6'5" I still have my issues with this.

2) In order to support the bike side to side gear is removed (making the bike less likely to topple) and the rainfly lines are wrapped several times around the seat, top tube, or wherever else they contact the bike and then staked down on the both  sides of the bike. This means the bike is both supporting the rainfly and being supported by the rainfly

3) security... obviously noone is going to be able to walk away with your bike at night if it's both supported and tied into the structure.

4) ultralight... with the tarp and 4-6 needle stakes I can think of no lighter structure... of course I'd probably still use my bivy if it was raining, I don't trust a simple rainfly alone

5) protecting the bike... I personally don't protect anything but my leather brooks saddle from rain. The reason being I ride in the rain all the time anyway. However, if you wanted to protect your bike from the rain I'm sure you could get a slightly bigger tarp or even a second ultralightweight tarp and use this setup plus a second tarp over the bike or modify this setup so the tarp goes all the way over the bike

Oh, it just occured to me you might try an ultralightweight poncho as a tarp for protecting a bike from the weather... the key is bikes don't need to breath... thus plastic is fine. The only issue then is making sure you use a heavy enough poncho that it doesn't tear. This is an alternative to sill nylon, spiniker, cuben or other lightweight rainfly or tent materials... as these are unecissary given their need to breath.

6) alternative tree usage.... obviously this setup would greatly benifit from a nearby tree. 

a) the bike could be used against and secured against a tree

b) the bike could be used opposite the tree so both ends of the tarp are elevated

c) after securing the tarp to the tree the bike could be placed completely underneath the tar

-Mike