Altitude Sickness:
This is largely out of your control except for the process of acclimation which you can only accomplish if you have some time to spend at high elevation. By time, even just sitting around at Horse Shoe Meadow works. I experienced very bad sickness on my first attempt because I didn't have time to acclimate. I didn't have acclimation time the second attempt either, but did try Diamox and breathing techniques and was successful

Bears:
Bears are more scared of you then you are of them. The bears at Whitney are opportunistic thieves. They would love to steal your pack if left unattended--especially at Whitney Portal. Otherwise, once on the trail I'm not even sure I have ever heard anyone say they have even seen a bear say above Lone Pine Lake. I certainly have never heard of a bear attack in the area. If you see a bear, consider yourself lucky! I love seeing bears!