The only issue I can see with Shrink-wrapping your dome is Ventillation.
I know, you want to keep the dust out. But you have another bogieman to deal with, and that's HEAT.
0h yeah, I know, you think the big evil thing is that dust, and yah, it is a little bit of a PITA... but let me tell you, you get that nice, sealed, airproof dome out there, where, like a VW van on a hot day with rolled up windows, you're gonna cook. Bad. Wtih no way for that heat to escape, what you've built is a nice big oven.
I've used parachute before, and it has 2 issues which we've already discussed -
one, it's wind-resistant. Means, yeah, you're doing the same thing with something that, should the wind catch it right, will turn your Playa Hilton into a Flying Saucer. And while it MAY be the Playa, there are already enough flying saucer sightings out there to add yours to the mix.
Two - they're somewhat fragile, esp, bu the time they're old enough to become a surplus item. I *have* seen partially naked domes in real life from Parachutus Disintegratus... neither it nor yourgear will appreciate it.
However, saying that... there is a way I cam (and do) recommend them. Part one, when you set it up, put the little relief hole on the top. Seriously. The heat will somewhat chimney out of this, especially when combined with...
Part Two is make them so they roll up on the bottom, so you CAN get that airflow you're gonna so desperately want and need. Believe me, you're gonna say F*** the dust when temps outside are 95 and inside 30 degrees hotter. Actually, this is so important it should be number 1.
So, on to Part 3. Put a cover over the thing. I like winter or desert camo. Hell, we've done domes using winter camo as the cover. And you want that not laying on top of the 'chute, you want an air gap between the two... How? Couple ways.
(1) Build stand offs onto the outside of your dome. Kind of a slow PITA hassle, but you can then adjust your "shade and wind gap". AND you haven't eaten the inside of your space. But I kinda like better, this idea...
(2) Put the camo cover on the dome, and SUSPEND THE CHUTE FROM INSIDE THE FRAME. Same concept - you need the dual layer shade... but you get 2 (actually 3) advantages... One, you can put an additional shade layer on top of the camo net (which is better, (2) you get the "pumping" action of the chute when the wind comes up WITHOUT the chute wanting to do a Mary Poppins, as your frame will retain your chute (which helps it longevity-wise as well), and (3), instead of looking like a fucking dome, it takes on the appearance of an arabian tent-esque interior. Or at least mine did.
Now... you wanna be SUPERcool?
Build a second dome which is 1' diameter larger than your original dome... and cover it with the most renowned shade cloth and dust-trapping material inveted - aluminet Shade Cloth. I personally LOVE that stuff, it has this glimmery silverishness abouut it that screams cool, and it really DOES a good job blocking ol' Mr. Sun, but it comes with a warning - it is THE biggest dust magnet known to Burnerdom. Doubt me? Help take down an aluminet covered anything... without goggles and a mask. Oh he,, WITH goggles and a mask. But it works. (BTW - My old friend, Uncle Camonet, either in Snow or Desert colors, works almost sorta just as well.)
Just IF you do this, make sure they're the same "phase" say, a pair of 2v's, not a 2v and a 5/8 3v.... otherwise you may have geometric hell to pay!!. I kinda like the above combo, BTW, you cann make a cool dome with a nice insulation space between them, but you MUST have your measurements dead on, otherwise you won't fit one inside the other, which is awfully embarassing. (Oh yeah, if you do this.. make SURE you color-code your poles and parts (you should do this anyway on anything more than a 1v) because you don't want your parts all mixed up, and spend 4 days wondering why your double dome delight not only isn't working, but you have a clusterfracking mess as well...)
You can also default to #83b - get a costco tent garage and put your dome inside that. OK, it's kinda sorta cheating, but there's a reason you see so many of these things out there.