Lets see if I've got this stuff right. We often discuss the caliber and model of guns to use in bear country. Only a fool goes hunting a real honest bear with a handgun. And then only as a stunt to prove it can be done. The smarter fools bring along a friend with a serious caliber rifle. Yes, .30 caliber rifles can be serious, but those often are called magnums and push a 200 or so grain bullet beyond 3000 fps. So bear gun threads are usually centered on handguns to haul all over gawd's creation all the while hoping against all hope we won't be seeing one. Serious hunters already know how to select a rifle for the task.
Here the OP is considering blundering into the brush with an inadequate caliber to pit himself against an unknown. Also unknown is the mood of the critter he blunders into. Its different if you have the element of surprise. Not sure how much different because if you surprise the bear, he may just decide you're on his turf.
I'd suggest the OP invest in one of the little heat seekers. I don't remember what they're called, but it looks like a flashlight. Its got PIR (Passive Infra Red) out in front. Its like a hand held motion detector alarm. The one I bought also has a red laser that aims at the warm spot.
I think it was initially marketed as a game finder. The theory being that if you up and wounded or killed a critter, its remaining body heat would set off the device. The button is to activate the red laser so you could tell which bush held the now dead critter, or live and angry bear. Just hope its not a mountain lion that dislikes playing with red laser dots. If you really think you've got something just out of your lawn, it might do what you seek. Or just put up motion flood lights to let it see into the bushes where you can't. Yes, they can often see through foilage.
As for the relocation ideas....they stink. I keep remembering the events out in Moab, UT about 20 or so years ago. This lady had a yard. Yards are hard to grow in the dessert, and folks don't take kindly to some critter tearing them up. So the lady finally got mad and called animal control. You know the guys, they drive around and try to capture unlicensed pups. Well they came out and visited her and were told a large yellow dog was running through her yard at night. It was even tearing up her grass, which was why she called. So taking it all at face value, they selected their biggest trap, baited it and left. The next morning the lady was calling, kind of hysterical. They caught it. It was big and yellow. But it wasn't a dog, it was a mountain lion. So the cavalry rushed over and saw their formerly rectangular cage had been pulled mostly into a ball, and the resident was pretty intent on getting out. Folks are weak, full grown mountain lions aren't weak.
So they used their finest tranquilizer gun and gave it a nap. Then they drove it up in the LaSal mountains and released it. But since it was chemically asleep, they stuck around until it woke back up. It was a bit confused, but it was time to leave it alone. The fun part was it took it 2 full weeks to wander its way back to town. Guess it was a city critter. Relocation sometimes doesn't work.
