Fromy my experience, they aren't great at stealth. I once had them in a hotel room, they came crawling towards me as soon as I laid down. I killed the first two and fled. Got a different room at the same place that was not infested (it was late and I was poor then). No bedbugs came home with me though I did put clothes in the freezer just in case.
It really depends on how severe the infestation is, and how long it has been since the bugs had a meal. Very hungry bedbugs will come out in the open, less hungry ones will wait until the middle of the night to feed.
I do wonder how very hungry bedbugs exist in a hotel room. But the evolutionary pressure against gratuitously running over an uncovered bedsheet while the light is on is pretty clear, too.
I do a quick bedbug check (headboard, nightstand, boxspring) in hotels I visit and mostly don't worry about it.