I now know that it's possible to transport (filled) mylar balloons by bicycle. A buddy's birthday is today, and I figured he needed some Spiderman and other assorted balloons to celebrate, so I stuffed four of them in a large trash bag, and then tied the drawstring to the rear rack.
Worked just fine as long as I kept my speed down. Kinda funny how much they deflated in the cold air (science!).