Generally speaking, yes, assuming that you follow the rules of the park. Venturing into the backcountry, with or without bears, always comes with certain risks, which can be minimized by following basic safety procedures. The number one rules with respect to bears apply to food and anything with a scent. Bears have super sharp sense of smell (they can smell through a tin can), so you need to be sure to store food outside of your tent. For a complete list of the rules, check out the following link to a section about bears and food storage at Yosemite: 

http://www.nps.gov/yose/planyourvisit/bearcanisters.htm  

Also, there's a short video of how to be safe in bear country on the home page of OhRanger.com.  Have fun in the park and be sure to share your experience with the rest of the park-loving community at OhRanger.com.