Bed bugs can lay dormant for one year so I'm afraid 24 hours in the garage won't do much. Laundry will help kill the eggs if the water's really hot. Not sure the dryer is quite enough, but it's better than nothing I guess...
If you are *really* terrified you can get a bug-proof casing for your mattress. (In fact, you can ask me to give you one - my husband would NOT tolerate it and kept thinking that it made plasticky sounds... I did not think it was that bad.) It's the most obvious hiding spot for them and will prevent most problems supposedly...
When we were in Paris last year I inspected everything in the hotel room when we checked in (mattress seams especially) and couldn't find anything, however the first morning I found a dead bed bug (positively identified) on the bed. No traces of blood anywhere, no feces, nothing but a single dead bed bug. (I kept the dead bug and used it to bargain a deep discount on the room price later on.)
Needless to say, we were freaked out, but there was no way I was going to try finding another hotel in Paris for the remaining two nights, and the other place would have been just as likely to have bed bugs, as every hotel of every major city in the world does. When we landed back home, everything went straight to the hot cycle in the washing machine (even what was not supposed to - that's life!) and our bags were thoroughly inspected and vacuumed outdoors.
Later that summer, I started getting bites on my extremities, often two in a row. (Bed bugs are well known for taking three in a row, also known as "breakfast, lunch and dinner" when they are disturbed in their blood-sucking activities.) Freaked out even more. It took me a while to realize that the bites were occurring after my night shifts volunteering at the aquarium, and that's probably where the bites originated. [For Badger's: I always wondered what the kids brought from home when they came for sleepovers.... But maybe it was just from outside when I checked resp rate at the surface.] In the meantime, we cleaned everything EXTREMELY THOROUGHLY in the home, vacuumed every crack obsessively, and covered our mattress with the aforementioned mattress cover, which my husband despised.
We never saw a bedbug again, but they terrorize me still.