I found some bedbugs at a hotel on a business trip once, and since then I've been paranoid like no one's business (seriously, on that trip I wouldn't even sleep under the covers on the bed, even though my new room checked out just fine).
In addition to checking the bed when you get there, don't forget to check drawers and curtains! Sometimes they hide there as well. Something else I do now: Before every trip, I buy those 2+ gallon Ziploc or Glad plastic bags. Any clothing not hung in the closet gets stored in those. When I need something, I take it out of the bag, and I keep additional bags on-hand for dirty clothes. I also put other items in the bags. It may not help if my suitcase gets one, but at least it helps lessen the chances of picking them up on clothing. Oh, and ALWAYS keep your suitcase on a luggage rack or in the bathroom during your trip. If you're feeling super creeped out, you can also buy those GIANT plastic bags that technically for storage, but a suitcase will fit in them... (yes, I've done this)
When we get home, if it's hot enough I usually let our suitcase sit in the hot car for a day because that will help kill them. If it's super cold when you get home, you can also sit the suitcase in the cold car for 24-48 hours. Then everything goes straight from the suitcase to the washing machine, and on hot. If you're worried about dyes running, buy those Shout Color Catcher things. They work great.
It's really, really gross, but the best way to prevent bedbugs is to just do your homework. There are a lot of resources online to help identify them, know what signs to look for, etc. At the first hotel (and thankfully only hotel) I found the bedbug signs, I called the front desk. Understandably, she was wary and asked if I was SURE that I was looking at a bed bug shell (which was right next to a blood trail). I told her, "If it's not a bed bug shell, then it's a really nasty booger." She moved me with no questions after that.