I object to you calling the guy with bedbugs a filthy pig, as I once had the displeasure of bed bugs getting into my apartment, even though I'm the cleanest neat freak I know. In an apartment or condo building, especially in older ones with radiators that go from unit to unit, those little bastages spread like wildfire.
The key to keeping it under control is exactly what your condo board is doing. The way to let it spread around the building, like herpes in a whorehouse, is for the useless idiot building managers to secretly spray only the affected suite and hope for the best. Because the best wont happen, the worst will. They get behind the baseboards and into the walls and go from suite to suite. Up, down, across the hall. No kidding.
So just be happy that your condo board is protecting your stuff and your peace of mind. Let the exterminator into your suite, and don't worry about the chemical. Those guys have been in thousands of suites before. They don't care about your dildo collection, or whatever it is that you're afraid they'll see.
Seriously, it's probably best if you take Rover to a friend's place, as the spray needs an hour or something to dissapate. If they have to spray it, they have to spray it that day, as they'll be spraying all the other affected suites. It's not effective to not do it all at once.