There is a myth that needs to be put to bed.  Bears are not short sighted. (Nobody ever asked the bear) I have been sight hunted/followed, from more than a quarter mile away on the North Slope.  We were strangers on the land(Surveyors) in the midst of a band of Caribou whom immediately left when they saw us.  The  bear was upwind so he was relying on sight and from the first time we saw him he was homed in on us. 
Consider this, a thirty thirty rifle is well known to be inadequate for bear, has a muzzle energy of 1900 foot pounds, a 44 magnum has a muzzel energy of around 850 foot pounds.  We have clocked a bear with a helicopter at 45 miles an our (same bear as above, after helicopter picked us up) that is 45 feet per second.also the 44 mag is notoriously hard to get an aimed second shot off in less than one second.  As much as they are loved, a 44 Mag is a puny firearm with a lousy rate of fire.  I prefer a long magazine 12 gage with slugs first then shot. I carry bear spray also.