I guess I must be a really careless parent given all these "no way" replies.
When DS was 9 months old, DH and I had an opportunity to fly out to San Francisco. We took DS with us and while we were there, we asked the hotel to recommend a baby-sitting service. This lovely grandmotherly woman came to our hotel room and stayed with DS while we went out for an adults only dinner. After speaking with her for a short time while DS got used to her I learned that she was a retired school teacher and that she had gone through security checks (fingerprinting and such) in order to get a job with the service.
DH and I went out for a lovely dinner and when we got back to our room, the sitter had DS sound asleep in the crib and she was watching television with the sound turned down and only the light in the bathroom on. She was a doll and worth every penny we paid her. I wanted to pack her up and bring her home in our luggage!
So although I'm not 100% sure I'd just use a friend of a friend, I'd definitely consider asking at the hotel if they have a baby-sitting service they recommend. Foortunately my kids are now too old to me to have this problem anymore.