Bobcats are everywhere. Get used to it. I went a lot of years catching up to a dozen a year. They are pretty stupid, so not hard to trap. Most have a pretty large home range, so the key is a trap might have to set for a while. My own personal observations are that a female cat takes about two weeks and a male cat takes a month to cover his territory. Females with young will stay in a smaller area and capitalize on a food source, like unprotected chickens. There are usually two females and one male in a home range, young males travel until they find a vacant home range, and often show up in marginal habitat. When you trap one, or more, you are opening up territory for a new cat to move in, and one will, pretty soon.
What people are referring to as "leg traps" are actually foothold traps. Perfectly humane if selected and used properly. Non target catches can be released unharmed.Anything that would catch something by the leg would not be very effective, you are looking for a pad catch to prevent the animal from escaping. The proper trap means the animal will not fight the trap very much, which means it will be there waiting for you. Selecting the wrong trap, and not tuning and setting it properly means that the animal will fight the trap, break it's leg, escape, etc. none of which are desirable outcomes for anyone engaged in trapping animals. It's not cartoons, there are no serious trappers or wildlife biologists using huge tooth jawed bear traps that reach half way up a caught animal's leg. Foothold traps are used successfully to harvest animals, as well as to collar and release animals for study and to catch animals for restocking.