Mark, yeah, bobcats are cool. That bobcat IS home. You don't have to encourage it to stay. They have a small territory, especially the females, and will not go far as long as there is food. Even if the food supply shrinks, and they move away, the food supply will grow back, and they will be back.
It's really important to never, ever feed a wild animal. Mainly because the type of food and the food levels at different times of year trigger important functions in animals, such as fur shedding to be cooler in summer, or fur growing to be ready for winter, or if there's not much food it won't have as many babies at once, or if there's a lot of food it will have more babies. But if it has more babies because you've been feeding it, then those babies may not have enough food. Natural food is what its body relies on to be healthy, not our food, not food we bring in that isn't local.
It's really important to be able to survive with existing food levels. It stays in shape by hunting, it learns about its environment and the other wild animals it must coexist with. It gets its immune system built up by what it eats locally, and shouldn't give up eating native food because it's getting human food.
It also isn't fair to encourage a bobcat (or any wild animal for that matter) to stay in a territory that is overlapping with other animals' territories if those animals have already duked it out and established territories. We have a fox couple that once a year becomes a fox family and will get into fights with the local bobcat. They have worked it out, and manage to overlap, but the cameras have shown us that although the bobcat fought hard in the moment of that territory establishing, it didn't hang around as much while the foxes were raising babies. And that's only fair to the foxes, because they, too, are great hunters of rodents. The bobcat didn't entirely leave, and shows up more now that the fox babies have grown up and moved on.
There are plenty of animal characters around to be worthy of living with. These animals are so much more aware of us than we are of them, and about their environment, don't even worry about them. Mother Nature has had it figured out for eons, so this is how we coexist with them.