For what it's worth, at least 7 climbers have died in Denali this year so far. Most years no one is killed by a bear anywhere in the state. If there are a million people that visit bear country in Alaska in a year and one is killed, and 1,500 permits for Denali and on a typical year maybe 3 are killed, the odds of dying on Denali are 1 out of 500, and the odds of being killed by a bear 1 out of 1,000,000, making Denali 2,000 times as dangerous than bears.
I believe the risks of Denali tend to be under rated, and that of bears highly over rated.
Good luck with both parts of your adventure. Reasonable chances are worth taking.