I've used a .375 JDJ Contender for 18 years, taking game as small as about 15 lbs., to as heavy as about 2000 lbs. I've generally used the 270 Hornady Spire point for most game, but have also used and would recommend the Horn. 220 FN for whitetails and similar sized animals. Naturally, recoil is a lot milder, too, with the 220 than with the 270 or the 300 FMJ.
Bears? Well, there are bears, and there are BEARS. I prefer the .475 Linebaugh for them, but have shot one large Blackie using a .375 JDJ and the 270 Horn. I hit him at about 75 to 85 yds. in a salmon filled stream in SE Alaska, penetrating a lung and breaking the off-side leg. He immediately hit the " bear tunnels" next to the stream, filled with alders, devil's club, and other vegetation, travelling perhaps 100 yds. through those tangles. I followed quickly and finished him with a FA .475 Linebaugh.
A .475 is the only handgun I've used on bears since, but that's just me.
The .375 JDJ is a great cartridge. Go get a barrel. By the way, taking note of your handle, I must say that the .338 JDJ is another great and versatile one.