They make crappy trunk racks that strap on. I'd give you mine if you lived nearby.
If you are loading a bike daily, then it's dumb to rule out installing a hitch. A hitch is the best way to mount a bike, and it doesn't cost much. Often about $125 or so, and they are super easy to install (typically 4 bolts).
I use my hitch all the time for transporting bikes, hauling a trailer, and just recently I towed a stranded vehicle off the freeway and into a parking lot.