I use Sen-Sci volcano style traps.
The pros: these are NOT sticky traps. They are not attractive to other bugs/pests, and I've only once found a dead spider in one. Guess he just crawled in for kicks 'n giggles and never made it back out.
The cons: haven't found any yet, other than they are a little pricey ($15 for the trap, $10 or so for a packet of refill baits), and last time I tried to buy them I had to go thru a licensed pest control supply company. They didn't care: I'm a land lord so they just set up an account for me. You can also buy them on Amazon, I think, without any trouble, though. Haven't tried that yet, but I did see them available a few months ago. I have a decent supply so not running out.
Here's the rub: you cannot PROVE a house is bug free. May the trap worked. Maybe it didn't. Maybe you put it down 5 minutes before the tenant showed up. How can you PROVE that both it and you did everything you're guaranteeing it did?
Easy, you can't. Unless you also want to set up a camera and have the tenant watch days of video showing when you put down the traps, didn't disturb or empty them, up until the time they show up at your front door.
But what you CAN do is show that you are doing a reasonable level of due dilligence. Proofs aint the issue: evidence is the issue.
Judge: Mr. LL, Did you do anything to mitigate the risk of bedbugs in this house?
LL: Yes your honor, we installed these traps that are attractive to bed bugs. They are professional grade traps used by companies X, Y, and Z here in our fair town. We found nothing in them.
J: Okay, Mr Tenant, did you sign the lease saying you saw these traps empty at move-in?
Tenant: Yes, your honor, but there were bugs later.
J: Well, then the most likely cause of those bugs is you brought them in. Cost of treatment is the Tenant's responsibility. Judgement in favor of the LL.
That's the best scenario you can hope for. Judges aren't in the business of conclusively determining fact vs. fiction with 100% certainty. They are in the business of deciding whose story to believe. Have your evidence and make a convincing argument.