Your idea of a .357 levergun is perfect. I've got one and it does a lot things nicely. Just make sure the gun will cycle both .38 special and .357 mags and you have something for everything. I don't know how big the black bears are in your country, but the .357 is more potent than some give it credit for. A similar levergun in .44mag/special is also a great choice. For me, a "walking around rifle" needs to be light and handy and the levergun works.
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