I went through the process with Marriott about two years ago and have nothing but positive things to say about how their central insurance/risk management team handled the situation. As you said, they confirmed within 24 hours that the bedbugs were present - although in my case I had photographic evidence and checked out of the hotel as a result, so it wasn’t exactly controversial.

Compensation (other than obviously comping the stay) will be a negotiation, but I feel I was treated fairly in the final reckoning. If you feel your bites are bad enough to warrant medical care, seeking that ASAP will be a good idea so you have documentation of that. Pest control for your home, if necessary, will also likely be on offer. Once all the expenses are known they will move on to figuring out numbers. Points and cash are both possible, so if you value one more than the other, think about that in advance.

I suspect they are generous and fair in this process because treating a guest well beats getting lawyers involved for everyone. Still, I was impressed by the professionalism.

On a practical level, the best way to deal with possibly brining bedbugs home is not dry cleaning or other surface cleanings, it’s heat treatment. I bought a ZappBug oven and it works well, although their stock thermometer is junk and you should buy your own. Bury it deep in your stuff and make sure the whole object gets up to 130 degrees as per the manual, not just the exterior. Great peace of mind though, and not even very expensive... combine that with the bed leg bug traps that elevate your bed using a platform they can’t climb and you should be home free. Of bugs.