depending on YOUR tolerance to recoil ,and , assuming you will be in a stand.300 grain JSP bullets and 3031 powder.Starting with 43gr. for 1550 fps and max load of50 gr for 1830 fps. A 405 jsp with3031 starts at 38.5 gr =1312 fps and max load of48 gr =1736.
If you want to shoot cast bullets try some Lyman 457122 HP's. These loads require a dacron wad of about 1/2 grain(.5 grain) to hold the powder near the primer in the loaded case. 47gr 3031=1723 fps to start and a MAX load of54 gr 3031 =1934 fps. There ARE hotter loads ,but bear are not that hard to kill.
These loads are from a 24" barrel,and are safe in MY guns (T/C contender and Mauser bolt rifle) They are from a Lyman book and deemed safe for 1886 Win & 1895 Marlin.
I have also used an LBT bullet,420 grain pointed ,gas checked design to take bear and deer with IMR 3031 :-D