My mother is trying to locate a lost cat and wants to rent/hire a bloodhound dog.
I've been involved in tracking work for nearly 30 years. I've taught it for nearly 20.
First. It doesn't have to be a bloodhound. There are lots and lots of dogs that are able to search for an animal or child.
There are not a lot of people who do this type of thing, simply because of the time versus the cost. Additionally, there is simply the situation that the dog doing the search may simply come up empty, so to speak.
Depending on where you're located, try to get in touch with some of the local tracking people, or search and rescue people. Although they don't do this type of work, it's the type of question that we get ALL the time.