Congratulations on buying a 44 magnum, you have picked a winner! Usually the first piece of advice you will get is to do the "poor" mans trigger job to your new sixgun. That is, drop one leg off the main spring. Its too bad people keep saying this. There are two springs for a reason, dropping one off will lighten the trigger yes, but it will not make a bad trigger into a good trigger. If you want a good, crisp, repeatable trigger have a good gunsmith do it right, you won't regret it.
Becoming a good handgun shot starts with a quality trigger, that & practice will get you there.
Most any of the 240 gr. or bigger jacketed slugs have a good reputation on deer size game. Hornady XTP's are very popular. Bears come in two sizes, spring bear & fall bear & there can be a huge difference. A spring bear looks big because the hair is long but a 4 months nap will have him pretty trimmed down so the same bullet you used on your fall deer hunt will work. If its a fall bear then a bigger, tougher bullet usually works best. The Speer 270 gr. Gold Dot, the Barnes X bullets, etc. something on the bonded core side that holds together & gives great penetration. Many times bears don't bleed much, that long hair can plug holes pretty good. Breaking both front shoulders is a good idea if possible. I much prefer cast & I have taken bears with angling shots where a jacketed bullet might not get the job done but thats just me, others will chime in.
Check with Robb Leahy at Simply Rugged for a good shoulder rig.
Dick
Last edited by sixshot; 09/20/2015 6:21 PM.