shrek,
If I was going just for bobcats, I would get a rifle in the 17 call or 20 cal.
The new 17 Fireball, 17 Ackley Hornet, 20 Fireball, 20 Ackley Hornet, I would even go with a 204 Ruger. Small, fast, light jacket bullets without an exit.
Although I know people that use a 243 Win with an 75 to 80 grain bullets and not have an exit.
I see you have a 22-250 in the works, you could load your rounds down to minimum, and a really light bullet, like the varmint grenade, or a VMax in 40 gr, that should work great.
Good Hunting,
Gary