I worry about bed bugs. I've never really worried about them but there has been so many stories lately and then one of my best friends found out his apartment was infested a week before my trip last month so they were on my mind when I went to LA. He bought a sofa on craigslist and didn't check it out properly. He has a friend staying with him who sleeps on the sofa and that allowed the little pests to have a feast every night and multiple. My friend has cats so the guest always assumed fleas for the skin irritations and marks. The cats do not have fleas and things got out of hand quickly.
There are many websites and videos out there that offers tips. Many of them I think are a little extreme but they can give you some ideas of how to protect yourself. My suggestions would be to buy those space saver/vacuum bags. Not only do they protect your clothes from bed bugs but they can save you room in your luggage too. I actually bring a few and they came in handy at the end of the trip so I didn't have to mix dirty clothes with the clean ones for the trip back home.
Inspect the room when you arrive especially the mattresses and head board. I stayed at 4 different hotels on my last trip to the LA area and although I never found bed bugs, one hotel in particular I found dead beetles under the sheets and an empty box of condoms in the nightstand! I got a refund but the lesson is to check out the room before unpacking.
Keep your luggage on the luggage racks. Do not put your luggage on the bed or sofas. Bed bugs need to be close to their victims so I try to keep what I bring in (luggage, clothes, laptop) on the luggage rack and/or the closet away from the bed. Now I've always been this kind of person who likes to keep all my stuff in a hotel room consolidated into one area so this isn't something I just started doing. I don't like it strung all over the room. I don't like the idea of housekeeping have to work around all my stuff (or snoop through it) and this way, I don't have this mad dash to gather everything and get ready on check out day.
And I have talked to people at the front desk at every hotel I've checked into about how they deal with the issue of bedbugs. I don't do it in a rude way and explain how I do this at all hotels even if I was staying at a lavish 5 star resort. No hotel wants the bad reputation for bed bugs so most will be happy to tell you how they deal with the issue and so far, I've never experienced anyone who took an attitude with the questions and all seem to understand the concern. Of course, not matter what they do, a bed bug(s) can be brought in at any time into the hotel by other guests but it is reassuring when the hotel is at least proactive about the issue.
And when you get home, wash everything in hot water and dry in high heat if possible. Keep your luggage you bring home away from your bed and sofas until you can inspect them.
So hopefully these tips may help but please don't let it ruin your travel. I don't think there is anything wrong with taking precautions but don't let it get out of hand. I know it's sometimes easier said than done. After my last trip where I was very proactive about protecting myself from bed bugs and not having found evidence of them, my anxiety level has lowered.